MikaStars39/nano-eval huggingface dataset:
In the design of a pile-anchor structure for a certain project, a single row of anchor rods is used. The initial conditions are a design horizontal tensile force $T_{\mathrm{d}}$ of 400 kN, a free length of $l_{\mathrm{f}} = 6 \mathrm{m}$, a diameter $d = 150 \mathrm{mm}$, and an inclination angle $\boldsymbol{\theta} = 20°$. Starting from the anchor head, the soil layers penetrated by the anchor rod have the following parameters: the first soil layer is cohesive soil with a thickness of $h_{1}=3 \mathrm{m}$ and a liquidity index $I_{L} = 0.5$; the second soil layer is fine sand with a thickness of $h_{2}=5 \mathrm{m}$, in a medium dense to dense state. Utilizing a secondary grouting process, the friction resistance values are taken from Table 4.4.3 of the Chinese "Technical Code for Building Excavation Support" (JGJ 120--1999). The friction resistance is considered to increase by 20% after secondary grouting. The question asks for the calculated length of the anchor rod, which is () m.

Options:
A. 25.0m
B. 24.0m
C. 22.0m
D. 16.5m
E. 15.0m
F. 20.5m
G. 23.5m
H. 18.5m
I. 21.0m
J. 19.0m
Answer: C
The site of a certain highway bridge is located in a seismic intensity zone of 9 degrees, composed of medium sand with approximately zero clay content, and a groundwater depth of 1 meter. During a standard penetration test conducted at $4 \mathrm{m}$, a blow count of 23 was recorded. The reduction coefficient for the friction angle within the sand layer at this test point is ().

Options:
A. 5/8
B. 5/6
C. 4/5
D. 1/2
E. 3/4
F. 3/5
G. 2/3
H. 2/5
I. 3/8
J. 7/9
Answer: G
Male, 26 years old. Passed tarry stool for 2 days, worsening with dizziness and palpitations for half a day before emergency hospital admission. No history of liver disease, no recent medication history. Physical examination: BP 70/40 $mmHg$, heart rate 120 beats/min, abdomen soft, no tenderness, liver and spleen not palpable under the ribs, extremities cold to the touch. The most likely diagnosis for this patient is ().

Options:
A. Colorectal Cancer
B. Viral Hepatitis
C. Irritable Bowel Syndrome
D. Hyperthyroidism
E. Peptic Ulcer Disease
F. Pancreatitis
G. Chronic Kidney Disease
H. Gastritis
I. Duodenal Ulcer
J. Appendicitis
Answer: I
The numerical aperture of a microscope's oil immersion lens is 1.5. What is the minimum resolvable distance when using a $250nm$ ultraviolet light source?

Options:
A. $$
9 5. 5 \mathrm{n m}
$$
B. $$
1 5 0. 3 \mathrm{n m}
$$
C. $$
2 3 0. 8 \mathrm{n m}
$$
D. $$
1 2 0. 0 \mathrm{n m}
$$
E. $$
1 0 1. 7 \mathrm{n m}
$$
F. $$
2 0 5. 9 \mathrm{n m}
$$
G. $$
1 1 5. 6 \mathrm{n m}
$$
H. $$
1 3 4. 4 \mathrm{n m}
$$
I. $$
3 0 0. 0 \mathrm{n m}
$$
J. $$
8 8. 2 \mathrm{n m}
$$
Answer: E
An uniform disk with mass $m$ and radius $R$ is placed on a rough horizontal table. It rotates around a vertical axis through its center with an initial angular velocity $\omega_{o}$. Given that the coefficient of friction between the disk and the table is $\mu$, how long does it take for the disk to come to a stop?

Options:
A. $$
\frac{\omega_{0} R} {4 \mu g}
$$
B. $$
\frac{3 \omega_{0} R} {4 \mu g}
$$
C. $$
\frac{3 \omega_{0} R} {2 \mu g^2}
$$
D. $$
\frac{3 \omega_{0} R^3} {4 \mu g}
$$
E. $$
\frac{\omega_{0} R} {2 \mu g}
$$
F. $$
\frac{\omega_{0} R^2} {4 \mu g}
$$
G. $$
\frac{2 \omega_{0} R} {4 \mu g}
$$
H. $$
\frac{3 \omega_{0} R} {8 \mu g}
$$
I. $$
\frac{3 \omega_{0} R} {4 \mu^2 g}
$$
J. $$
\frac{3 \omega_{0} R^2} {4 \mu g}
$$
Answer: B
Monochromatic light is incident vertically on a single slit, and the third-order bright fringe of its diffraction coincides with the position of the second-order bright fringe when light with a wavelength of $600 \, \text{nm}$ is incident on the slit. Determine the wavelength of this monochromatic light.

Options:
A. $$450.0(nm)$$
B. $$475.0(nm)$$
C. $$428.6(nm)$$
D. $$520.0(nm)$$
E. $$410.0(nm)$$
F. $$350.0(nm)$$
G. $$480.0(nm)$$
H. $$550.0(nm)$$
I. $$600.0(nm)$$
J. $$500.0(nm)$$
Answer: C
Two pure fractions with relative molecular weights of $2 \times 10^{4}$ and $3 \times 10^{4}$ are mixed to give a sample of $\overline{M_{\mathrm{n}}} = 2.5 \times 10^{4}$ weighing 1 gram. If this mixed sample is mixed with another pure fraction with relative molecular weight of $7 \times 10^{4}$, what is the number average relative molecular weight of the final sample?

Options:
A. $$
1. 9 9 \times1 0^{4}
$$
B. $$
2. 2 5 \times1 0^{4}
$$
C. $$
3. 8 9 \times1 0^{4}
$$
D. $$
4. 1 0 \times1 0^{4}
$$
E. $$
3. 4 0 \times1 0^{4}
$$
F. $$
3. 6 8 \times1 0^{4}
$$
G. $$
4. 5 0 \times1 0^{4}
$$
H. $$
6. 7 5 \times1 0^{4}
$$
I. $$
5. 6 0 \times1 0^{4}
$$
J. $$
2. 9 5 \times1 0^{4}
$$
Answer: F
What is the peak spectral wavelength $\lambda_{\mathrm{m}}$ emitted by young people at normal temperature, in micrometers? What is the peak wavelength when they have a fever at 38.5°C? What is the peak spectral radiance $M_{\mathrm{e, s, \lambda m}}$ when they have a fever at 39°C?

Options:
A. 9.44μm,9.29μm,$3. 7 3 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
B. 9.45μm,9.22μm,$3. 6 8 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
C. 9.20μm,9.35μm,$3. 8 9 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
D. 9.30μm,9.18μm,$3. 9 5 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
E. 9.25μm,9.42μm,$3. 9 8 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
F. 9.40μm,9.25μm,$3. 7 5 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
G. 9.36μm,9.30μm,$3. 8 7 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
H. 9.36μm,9.40μm,$3. 7 0 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
I. 9.50μm,9.28μm,$3. 9 1 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
J. 9.38μm,9.34μm,$3. 8 5 \times1 0^{-3} \ \mathrm{( W \cdot c m^{-2} \cdot \mu m^{-1} )}$
Answer: G
The known cathode light sensitivity of the GDB44F is $0.5 \mu\mathrm{A} / \mathrm{lm}$, and the anode light sensitivity is $50 \mathrm{A} / \mathrm{lm}$. When used over a long period, the allowable anode current should be limited to within 2 μA. Given that this PMT is a 12-stage $Cs_3Sb$ multiplier with a multiplication factor of $\delta=0.2 ( U_{\mathrm{DD}} )^{0.7}$, its supply voltage value is ().

Options:
A. 1254V
B. 1178V
C. 1053V
D. 1467V
E. 980V
F. 1342V
G. 1135V
H. 987V
I. 1620V
J. 2046V
Answer: C
A transparent dielectric film is coated on glass $( \varepsilon_{r}=2.25, \mu_{r}=1 )$ to eliminate the reflection of infrared light (λ = 0.75μm). If ultraviolet light $( \lambda=0.42 \mu m )$ is incident perpendicularly on the glass coated with this dielectric film, what percentage of the incident power is reflected?

Options:
A. 3.57%
B. 9.47%
C. 14.11%
D. 7.89%
E. 8.23%
F. 6.81%
G. 10.52%
H. 15.67%
I. 12.34%
J. 5.98%
Answer: A
Design a small optical fiber communication system using an LED light source, $\lambda_{0}=0.85 \mu m, \Delta\lambda_{0}=40 nm$, multimode fiber $n_{1}=1.5$, $\Delta=0.01$, material dispersion $\frac{d n_{1}}{d \lambda_{0}}=3.5 \times 10^{5} m^{-1}, \quad\frac{d^{2} n_{1}}{d \lambda_{0}^{2}}=3.5 \times 10^{10} m^{-2}$. If a step-index optical fiber is used and the transmission pulse rate is $10 Mbit/s$, what is the dispersion-limited maximum transmission distance $L_{\mathrm{max}}$?

Options:
A. 4898.2km
B. 3588.1km
C. 1500.3km
D. 2624.7km
E. 4364.8km
F. 3150.9km
G. 1827.7km
H. 2050.6km
I. 2999.3km
J. 732.6km
Answer: D
A recording acousto-optic deflector uses tellurium dioxide as the acousto-optic medium. It is known that the number of resolvable points $N=300$, the ultrasonic transit time $\tau=10$μs, and the operating wavelength $\lambda=0.6328$μm. What is the acousto-optic interaction length if the allowable non-uniformity of ultrasonic intensity within the operating bandwidth is 3dB?

Options:
A. 37.5mm
B. 61.7mm
C. 55.1mm
D. 25.6mm
E. 33.3mm
F. 29.8mm
G. 52.3mm
H. 40.9mm
I. 48.5mm
J. 44.2mm
Answer: A
The core of a certain reactor is composed of U-235, $H_2O$, and Al, with volume fractions of 0.002, 0.6, and 0.398 respectively. What is the total absorption cross-section of the core at $E=0.0253eV$?

Options:
A. $$
9. 1 ~ m^{-1}
$$
B. $$
10. 5 ~ m^{-1}
$$
C. $$
6. 3 ~ m^{-1}
$$
D. $$
11. 6 ~ m^{-1}
$$
E. $$
8. 4 ~ m^{-1}
$$
F. $$
3. 5 ~ m^{-1}
$$
G. $$
7. 9 ~ m^{-1}
$$
H. $$
4. 7 ~ m^{-1}
$$
I. $$
12. 0 ~ m^{-1}
$$
J. $$
5. 8 ~ m^{-1}
$$
Answer: E
In a certain power reactor, it is known that the average thermal neutron flux density is $2.93 \times 10^{13} \ \mathrm{cm}^{-2} \cdot \mathrm{s}^{-1}$. The macroscopic fission cross-section of the fuel $\Sigma_{f}^{UO_{2}} = {\bf 6.6} \ {\bf m}^{-1}$, and the macroscopic absorption cross-section in the lattice cell $\Sigma_{a}^{ma} = 8.295 \ \mathrm{m^{-1}}$. The volume ratio of the fuel to the lattice cell is $V_{UO_{2}} / V = 0.3155$. What are the equilibrium concentrations and equilibrium xenon poisoning levels of $\mathrm{^{135}I}$, $\mathrm{^{135}Xe}$, $\mathrm{^{149}Pm}$, and $\mathrm{^{149}Sm}$?

Options:
A. $$
1.34\times10^{21}~\mathrm{m}^{-3},~
3.72\times10^{20}~\mathrm{m}^{-3},~
2.00\times10^{21}~\mathrm{m}^{-3},~
5.80\times10^{21}~\mathrm{m}^{-3},~
2.085~\mathrm{m}^{-1}
$$
B. $$
1.40\times10^{21}~\mathrm{m}^{-3},~
3.60\times10^{20}~\mathrm{m}^{-3},~
1.95\times10^{21}~\mathrm{m}^{-3},~
6.00\times10^{21}~\mathrm{m}^{-3},~
2.080~\mathrm{m}^{-1}
$$
C. $$
1.36\times10^{21}~\mathrm{m}^{-3},~
3.71\times10^{20}~\mathrm{m}^{-3},~
1.93\times10^{21}~\mathrm{m}^{-3},~
5.77\times10^{21}~\mathrm{m}^{-3},~
2.082~\mathrm{m}^{-1}
$$
D. $$
1.36\times10^{21}~\mathrm{m}^{-3},~
3.80\times10^{20}~\mathrm{m}^{-3},~
1.97\times10^{21}~\mathrm{m}^{-3},~
5.70\times10^{21}~\mathrm{m}^{-3},~
2.083~\mathrm{m}^{-1}
$$
E. $$
1.45\times10^{21}~\mathrm{m}^{-3},~
3.75\times10^{20}~\mathrm{m}^{-3},~
1.90\times10^{21}~\mathrm{m}^{-3},~
5.60\times10^{21}~\mathrm{m}^{-3},~
2.080~\mathrm{m}^{-1}
$$
F. $$
1.42\times10^{21}~\mathrm{m}^{-3},~
3.78\times10^{20}~\mathrm{m}^{-3},~
1.89\times10^{21}~\mathrm{m}^{-3},~
5.75\times10^{21}~\mathrm{m}^{-3},~
2.086~\mathrm{m}^{-1}
$$
G. $$
1.44\times10^{21}~\mathrm{m}^{-3},~
3.69\times10^{20}~\mathrm{m}^{-3},~
1.94\times10^{21}~\mathrm{m}^{-3},~
5.74\times10^{21}~\mathrm{m}^{-3},~
2.081~\mathrm{m}^{-1}
$$
H. $$
1.50\times10^{21}~\mathrm{m}^{-3},~
3.90\times10^{20}~\mathrm{m}^{-3},~
1.85\times10^{21}~\mathrm{m}^{-3},~
5.50\times10^{21}~\mathrm{m}^{-3},~
2.100~\mathrm{m}^{-1}
$$
I. $$
1.38\times10^{21}~\mathrm{m}^{-3},~
3.70\times10^{20}~\mathrm{m}^{-3},~
1.96\times10^{21}~\mathrm{m}^{-3},~
5.66\times10^{21}~\mathrm{m}^{-3},~
2.084~\mathrm{m}^{-1}
$$
J. $$
1.39\times10^{21}~\mathrm{m}^{-3},~
3.73\times10^{20}~\mathrm{m}^{-3},~
1.92\times10^{21}~\mathrm{m}^{-3},~
5.79\times10^{21}~\mathrm{m}^{-3},~
2.082~\mathrm{m}^{-1}
$$
Answer: C
A Carnot refrigeration cycle absorbs heat at $-12^{\circ} C$ and releases heat at $40^{\circ} C$. If the heat pump absorbs 15 kW at a temperature of $-12^{\circ} C$, what is the heat release rate at $40^{\circ} C$?

Options:
A. 21.5545kW
B. 22.8545kW
C. 19.6545kW
D. 16.5545kW
E. 15.5545kW
F. 18.5545kW
G. 18.4545kW
H. 18.7545kW
I. 20.2545kW
J. 17.5545kW
Answer: F
A piston refrigerator with a cooling capacity of $50 \mathrm{kW}$ operates with a high-temperature heat source at a temperature $t_{\mathrm{H}}$ of $32^{\circ} \mathrm{C}$ and a low-temperature heat source at a temperature $t_{\mathrm{L}}$ of $-18 \mathrm{^{o}C}$. The refrigerant used is R-134a, and it employs a regenerative cycle. The suction temperature of the compressor is $0^{\circ} \mathrm{C}$.Find the heat load of the recuperator.

Options:
A. 8.21kW
B. 4.52kW
C. 8.76kW
D. 5.37kW
E. 10.10kW
F. 7.15kW
G. 9.34kW
H. 6.43kW
I. 6.89kW
J. 3.29kW
Answer: H
Under the conditions of 0.101 MPa and 293 K, air enters a reversible Claude system, except for the throttling process, and is compressed isothermally to 2.02 MPa and 293 K. Then, 60% of the main stream gas is diverted into a reversible adiabatic expander, while the remaining air expands through the throttle valve to 0.101 MPa via the stages of heat exchangers.
If this reversible Claude system is used as a refrigerator, determine the refrigeration capacity per unit mass.

Options:
A. $$80. 8kJ/kg$$
B. $$86. 9kJ/kg$$
C. $$84. 3kJ/kg$$
D. $$77. 4kJ/kg$$
E. $$85. 7kJ/kg$$
F. $$82. 6kJ/kg$$
G. $$90. 2kJ/kg$$
H. $$88. 1kJ/kg$$
I. $$79. 3kJ/kg$$
J. $$91. 5kJ/kg$$
Answer: F
Given the reflectivity of the output mirror of a continuous YAG laser $r_{1}=0.9$, the reflectivity of the total reflection mirror $r_{2}=1$, internal loss $\alpha_{i}=0.01 \, \mathrm{cm}^{-1}$, the stimulated emission cross-section of $\mathrm{Nd}^{3+}$ $\sigma=50 \times 10^{-20} \, \mathrm{cm}^{2}$, lamp efficiency $\eta_{\text{lamp}}=0.5$, focusing efficiency $\eta_{\text{focus}}=0.8$, absorption efficiency $\eta_{\text{abs}}=0.2$, intrinsic efficiency $\eta_{0}=1$, pumping wavelength $\lambda_{P}=750 \, \mathrm{nm}$, and upper state lifetime $\tau_{21}=0.23 \times 10^{-3} \, \mathrm{s}$. If the superradiance coefficient $\mathbf{n}=4$, calculate the input electrical power required to achieve an output power of 50W.
Answer is___.

Options:
A. $$
1. 7 \mathbf{k} W
$$
B. $$
3. 3 \mathbf{k} W
$$
C. $$
7. 9 \mathbf{k} W
$$
D. $$
5. 6 \mathbf{k} W
$$
E. $$
2. 5 \mathbf{k} W
$$
F. $$
4. 5 \mathbf{k} W
$$
G. $$
5. 0 \mathbf{k} W
$$
H. $$
4. 0 \mathbf{k} W
$$
I. $$
6. 2 \mathbf{k} W
$$
J. $$
2. 8 \mathbf{k} W
$$
Answer: B
There is an infinite-length channel with a width of $h$, with a small hole in its side wall. The volumetric flow rate from the small hole is $Q$, and the fluid flows parallel far from the small hole. Assume the fluid is ideal, incompressible, and homogeneous, and that body forces can be neglected. The complex potential and velocity distribution in the channel are ( ) and ( ), respectively.

Options:
A. $$
{\frac{Q} {3 \pi}} \operatorname{c o s} {\frac{\zeta^{1 / 2}} {\zeta+1}}
$$
$$
+ \frac{Q} {h} \textrm{c o s} \Big( \frac{\pi z} {h} \Big)
$$
B. $$
{\frac{Q} {\pi}} \operatorname{l n} {\frac{\zeta^{1 / 2}} {\zeta-1}}
$$
$$
- \frac{Q} {2 h} \textrm{coth} \Big( \frac{\pi z} {2 h} \Big)
$$
C. $$
{\frac{Q} {\pi}} \operatorname{l n} {\frac{\zeta^{2 / 3}} {\zeta-1}}
$$
$$
- \frac{Q} {h} \textrm{s i n h} \Big( \frac{2 \pi z} {h} \Big)
$$
D. $$
{\frac{Q} {\pi}} \operatorname{l n} {\frac{\zeta^{1 / 4}} {\zeta-2}}
$$
$$
+ \frac{Q} {2 h} \textrm{s i n} \Big( \frac{\pi z} {2 h} \Big)
$$
E. $$
{\frac{Q} {2 \pi}} \operatorname{l n} {\frac{\zeta} {\zeta-1}}
$$
$$
- \frac{Q} {h} \textrm{t a n} \Big( \frac{2 \pi z} {h} \Big)
$$
F. $$
{\frac{Q} {\pi}} \operatorname{s i n} {\frac{\zeta^{3 / 2}} {\zeta-1}}
$$
$$
- \frac{Q} {h} \textrm{t a n h} \Big( \frac{\pi z} {h} \Big)
$$
G. $$
{\frac{Q} {\pi}} \operatorname{s i n} {\frac{\zeta^{1 / 3}} {\zeta-2}}
$$
$$
+ \frac{Q} {2 h} \textrm{s i n} \Big( \frac{\pi z} {2 h} \Big)
$$
H. $$
{\frac{Q} {4 \pi}} \operatorname{l n} {\frac{\zeta} {\zeta+2}}
$$
$$
- \frac{2 Q} {h} \textrm{t a n h} \Big( \frac{\pi z} {h} \Big)
$$
I. $$
{\frac{2 Q} {\pi}} \operatorname{l n} {\frac{\zeta^{2}} {\zeta-2}}
$$
$$
- \frac{Q} {4 h} \textrm{t a n} \Big( \frac{\pi z} {4 h} \Big)
$$
J. $$
{\frac{3 Q} {2 \pi}} \operatorname{c o s} {\frac{\zeta^{1 / 2}} {\zeta-3}}
$$
$$
+ \frac{Q} {3 h} \textrm{c o s} \Big( \frac{\pi z} {3 h} \Big)
$$
Answer: B
In a straight pipe of length $L = 3.5 \mathrm{m}$, air is filled at a pressure of $p_{0} = 2.50 \times 10^{5} \mathrm{N/m}^{2}$ and a static temperature of $T_{0} = 288 \mathrm{K}$. Assume that the air is ideal, when the right end of the pipe is suddenly opened to atmospheric pressure of $1.00 \times 10^{5} \mathrm{N/m}^{2}$.
Along the Mach lines corresponding to $p = 2.50 \times 10^{5} \mathrm{N/m}^{2}, \; 2.00 \times 10^{5} \mathrm{N/m}^{2}, \; 1.50 \times 10^{5} \mathrm{N/m}^{2}, \; 1.00 \times 10^{5} \mathrm{N/m}^{2}$, the values of $M$ are ( ).

Options:
A. $$
0, 0. 1 6 2, 0. 3 7 8, 0. 6 9 8
$$
B. $$
0, 0. 1 5 4, 0. 3 6 9, 0. 7 1 0
$$
C. $$
0, 0. 1 8 3, 0. 3 8 5, 0. 6 8 4
$$
D. $$
0, 0. 1 7 5, 0. 3 4 8, 0. 7 0 2
$$
E. $$
0, 0. 1 6 0, 0. 3 6 0, 0. 7 0 0
$$
F. $$
0, 0. 1 7 1, 0. 3 9 0, 0. 6 7 9
$$
G. $$
0, 0. 1 6 8, 0. 3 5 8, 0. 6 3 8
$$
H. $$
0, 0. 1 6 5, 0. 3 7 7, 0. 6 9 0
$$
I. $$
0, 0. 1 5 9, 0. 3 7 2, 0. 6 7 5
$$
J. $$
0, 0. 1 6 1, 0. 3 9 1, 0. 7 0 4
$$
Answer: A
Gas particles dispersed in infinite space are attracted toward a fixed center, with the gravitational force proportional to the distance from the particle to the center of gravity. Given the total mass of the gas as $M$ and the gravitational attraction per unit mass at a unit distance from the center as $\mu$, the pressure at the central point under isothermal equilibrium conditions is ( ) .

Options:
A. $$
M \frac{\mu} {8 \pi^{3} R T}
$$
B. $$
M \sqrt{\frac{\mu} {8 \pi^{2} R T}}
$$
C. $$
M \frac{\mu} {4 \pi^{3} R T^2}
$$
D. $$
M \sqrt{\frac{2 \mu} {8 \pi^{3} R T}}
$$
E. $$
M \sqrt{\frac{\mu} {8 \pi^{3} R T}}
$$
F. $$
M \frac{\mu} {8 \pi^{3} R^2 T}
$$
G. $$
M \sqrt{\frac{\mu} {8 \pi R^3 T}}
$$
H. $$
M \sqrt{\frac{8 \mu} {\pi^{3} R T}}
$$
I. $$
M \sqrt{\frac{\mu} {4 \pi^{3} R^2 T}}
$$
J. $$
M \frac{\mu^2} {8 \pi^{3} R T}
$$
Answer: E
Given that in a cylindrical elliptical tube with a cross-section defined by $\frac{y^{2}} {a^{2}}+\frac{z^{2}} {b^{2}} \leq1$, the fluid motion has velocity only along the axis of the tube, if we take the tube axis as the $x$ axis, then the velocity distribution on the elliptical cross-section is
$$
u=c \Big( 1-\frac{y^{2}} {a^{2}}-\frac{z^{2}} {b^{2}} \Big), \ \ v=0, \ \ w=0,
$$
where $a, b, c$ are non-zero constants. Assuming the density $\rho$ of the fluid is constant, give the mass flux and momentum flux through a particular cross-section of the elliptical tube.

Options:
A. $$
\frac{4} {3} \pi\rho a b c, \quad\frac{1} {5} \pi\rho a^{2} b c^{2}
$$
B. $$
\frac{2} {5} \pi\rho a^{2} b, \quad\frac{1} {2} \pi\rho a b c^{2}
$$
C. $$
\frac{5} {3} \pi\rho a b c, \quad\frac{1} {8} \pi\rho a b^{2} c^{2}
$$
D. $$
\frac{3} {4} \pi\rho a b^{2}, \quad\frac{2} {9} \pi\rho a^{2} b c^{2}
$$
E. $$
\frac{1} {3} \pi\rho a^{2} b, \quad\frac{2} {5} \pi\rho a^{2} b c^{2}
$$
F. $$
\frac{2} {1} \pi\rho a b^{2}, \quad\frac{4} {8} \pi\rho a b^{2} c^{2}
$$
G. $$
\frac{3} {2} \pi\rho a b c, \quad\frac{1} {6} \pi\rho a b c^{2}
$$
H. $$
\frac{1} {2} \pi\rho a^{2} b, \quad\frac{1} {4} \pi\rho a b^{2} c
$$
I. $$
\frac{3} {1} \pi\rho a b^{2}, \quad\frac{1} {4} \pi\rho a b^{2} c^{2}
$$
J. $$
\frac{7} {4} \pi\rho a b c, \quad\frac{3} {7} \pi\rho a b^{2} c^{2}
$$
Answer: G
In the irrotational motion of a certain incompressible homogeneous fluid, the velocity potential is
$$
\varphi=-\frac{2 t} {\sqrt{x^{2}+y^{2}+z^{2}}}.
$$
If during the motion, the pressure remains at $p_{1}=1.2 \times 10^{5} \mathrm{Pa}$ at point (1, 1, 1), and the fluid density is $\frac{10^{3}}{9.8} \mathrm{kg} / \mathrm{m}^{3}$, what is the pressure at point $(x, y, z) = (4, 4, 2)$ after 20 seconds from the start of the motion ?
( Assume the coordinate units are measured in meters and consider the effect of gravity. )

Options:
A. 9.689Pa
B. 8.782Pa
C. 7.946Pa
D. 10.456Pa
E. 7.501Pa
F. 12.000Pa
G. 8.333Pa
H. 10.005Pa
I. 9.112Pa
J. 11.214Pa
Answer: I
A point with a distance $l$ from the center of a sphere with a radius $\alpha$ is occupied by an incompressible dipole of strength $m$, whose axis is directed towards the center of the sphere. Without considering body forces, calculate the net force exerted by the fluid on the sphere, given that the fluid has a density of $\rho$.

Options:
A. $$
\frac{3} {4 \pi} \, \frac{\rho a^{3} m} {( l^{2}-a^{2} )^{3}}
$$
B. $$
\frac{3} {2 \pi} \, \frac{\rho a^{3} l} {( l^{2}-a^{2} )^{4}}
$$
C. $$
\frac{3} {2 \pi} \, \frac{\rho a^{2} l} {( l^{2}-a^{2} )^{4}}
$$
D. $$
\frac{3} {2 \pi} \, \frac{\rho a^{3} l} {( l^{2}-a^{2} )^{3}}
$$
E. $$
\frac{1} {2 \pi} \, \frac{\rho a^{2} l} {( l^{2}-a^{2} )^{4}}
$$
F. $$
\frac{3} {2 \pi} \, \frac{\rho a^{3} l} {( l^{2}+a^{2} )^{4}}
$$
G. $$
\frac{3} {2 \pi} \, \frac{\rho a^{3} m} {( l^{2}-a^{2} )^{4}}
$$
H. $$
\frac{3} {\pi} \, \frac{\rho a^{3} l} {( l^{2}-a^{2} )^{4}}
$$
I. $$
\frac{2} {\pi} \, \frac{\rho a^{3} l} {( l^{2}-a^{2} )^{3}}
$$
J. $$
\frac{1} {4 \pi} \, \frac{\rho a^{3} m} {( l^{2}-a^{2} )^{4}}
$$
Answer: B
For monochromatic waves with a water depth of $h$, considering the effect of surface tension, how can the wave speed reach an extremum for any water depth?

Options:
A. When $h > \frac{\sqrt{3}}{k_{min}}$, there are no extreme values.
B. When $h = \frac{\sqrt{2}}{k_{max}}$, no apparent extreme can be observed.
C. When $h = \frac{\sqrt{3}}{k_{min}}$, wave speed always decreases.
D. When $h < \frac{\sqrt{3}}{k_{min}}$, there are no extreme values.
E. When $h < \frac{\sqrt{3}}{k_{max}}$, wave speed becomes infinite.
F. When $h = \frac{\sqrt{2}}{k_{min}}$, wave speed reaches its peak.
G. When $h < \frac{2}{k_{min}}$, there are no extreme results.
H. When $h > \frac{\sqrt{3}}{k_{max}}$, wave speed will oscillate.
I. When $h > \frac{3}{k_{min}}$, there are extreme values always present.
J. When $h < \frac{3}{k_{min}}$, wave speed becomes constant.
Answer: D
The equilibrium potential of a silver chloride electrode Ag|AgCl(s), KCl(0.5 mol/dm$^{3}$) at 25°C is().

Options:
A. $$
= 0. 3 5 02 \ \mathrm{V}
$$
B. $$
= 0. 1 8 75 \ \mathrm{V}
$$
C. $$
= 0. 3 0 17 \ \mathrm{V}
$$
D. $$
= 0. 2 8 31 \ \mathrm{V}
$$
E. $$
= 0. 2 9 86 \ \mathrm{V}
$$
F. $$
= 0. 2 4 05 \ \mathrm{V}
$$
G. $$
= 0. 2 5 08 \ \mathrm{V}
$$
H. $$
= 0. 2 7 14 \ \mathrm{V}
$$
I. $$
= 0. 1 9 08 \ \mathrm{V}
$$
J. $$
= 0. 2 1 39 \ \mathrm{V}
$$
Answer: G
At 25°C, the standard electrode potential for the Pb|Pb$^{2+}$ electrode is -126.3 mV, and for Pb|Pb$F_{\mathrm{2}}$(solid), $\mathrm{F}^{-}$, it is -350.2 mV. The solubility product $\mathbf{K}_{S}$ of Pb$F_{\mathrm{2}}$ is ().

Options:
A. $$
K s=6. 5 1 \times1 0^{-4}
$$
B. $$
K s=4. 6 3 \times1 0^{-5}
$$
C. $$
K s=7. 3 5 \times1 0^{-10}
$$
D. $$
K s=8. 2 9 \times1 0^{-8}
$$
E. $$
K s=3. 2 8 \times1 0^{-8}
$$
F. $$
K s=2. 6 3 \times1 0^{-8}
$$
G. $$
K s=3. 9 2 \times1 0^{-6}
$$
H. $$
K s=9. 0 4 \times1 0^{-11}
$$
I. $$
K s=5. 4 7 \times1 0^{-7}
$$
J. $$
K s=1. 1 8 \times1 0^{-9}
$$
Answer: F
At 25°C, a current of 0.01 A is used to electrolyze a mixed aqueous solution of 0.1 mol/L Cu$SO_{\mathrm{4}}$ and 1 mol/L $H_{\mathrm{2}}$$SO_{\mathrm{4}}$. The measured voltage across the electrolytic cell is 1.86 $\mathbf{V}$, and the overpotential for oxygen evolution at the anode is 0.42 $\mathbf{V}$. Given that the solution resistance between the two electrodes is 50Ω, the overpotential for copper deposition at the cathode is(). (assuming only copper is deposited at the cathode)

Options:
A. $$
= 0. 1 0 2 \mathrm{~ V}
$$
B. $$
= 0. 0 5 6 \mathrm{~ V}
$$
C. $$
= 0. 0 4 5 \mathrm{~ V}
$$
D. $$
= 0. 0 8 1 \mathrm{~ V}
$$
E. $$
= 0. 0 6 7 \mathrm{~ V}
$$
F. $$
= 0. 0 7 3 \mathrm{~ V}
$$
G. $$
= 0. 0 3 8 \mathrm{~ V}
$$
H. $$
= 0. 0 2 9 \mathrm{~ V}
$$
I. $$
= 0. 1 3 5 \mathrm{~ V}
$$
J. $$
= 0. 1 4 9 \mathrm{~ V}
$$
Answer: G
In an additive-free zincate solution, zinc plating occurs with a cathode reaction of $\mathrm{Zn(OH)_{4}^{2-} + 2e \to Zn + 4OH^{-}}$, and it is controlled by the diffusion step. At 18°C, the potential measured at a certain current density is 0.056 $\mathbf{V}$. If the reaction of hydrogen gas evolution on the cathode is ignored, and given that the diffusion coefficient of $\mathrm{Zn(OH)_{4}^{2-}}$ ions is $0.5 \times 10^{-5} \mathrm{cm^{2}/s}$, with a concentration of 2 mol/L, and the concentration gradient at the electrode surface liquid layer (at $x=0$) is $8 \times 10^{-2} \, \mathrm{mol/cm^{4}}$, the concentration of $\mathrm{Zn(OH)_{4}^{2-}}$ ions in the electrode surface liquid layer is().

Options:
A. $$
=0. 0 3 8 \, m o l / L
$$
B. $$
=0. 0 1 5 \, m o l / L
$$
C. $$
=0. 0 2 3 \, m o l / L
$$
D. $$
=0. 0 5 6 \, m o l / L
$$
E. $$
=0. 0 7 4 \, m o l / L
$$
F. $$
=0. 0 8 2 \, m o l / L
$$
G. $$
=0. 0 9 0 \, m o l / L
$$
H. $$
=0. 0 4 5 \, m o l / L
$$
I. $$
=0. 0 2 9 \, m o l / L
$$
J. $$
=0. 0 6 1 \, m o l / L
$$
Answer: C
At 25°C, when zinc is electrolytically deposited from a Zn$SO_{\mathrm{4}}$ (1 mol/L) solution at a rate of 0.03 A/cm$^{2}$, the cathode potential is -1.013 $\mathbf{V}$. It is known that the control step of the electrode process is the electron transfer step, with a transfer coefficient $\alpha=0.45$ and an average activity coefficient $\gamma_{\pm}=0.044$ for the 1 mol/L Zn$SO_{\mathrm{4}}$ solution. What is the exchange current density of this electrode reaction at 25°C?

Options:
A. $$
j^{0}=6 .9 \times1 0^{-7} \mathrm{A / c m}^{2}
$$
B. $$
j^{0}=9 .0 \times1 0^{-1} \mathrm{A / c m}^{2}
$$
C. $$
j^{0}=1 .1 \times1 0^{-6} \mathrm{A / c m}^{2}
$$
D. $$
j^{0}=3 .2 \times1 0^{-4} \mathrm{A / c m}^{2}
$$
E. $$
j^{0}=5 .1 \times1 0^{-3} \mathrm{A / c m}^{2}
$$
F. $$
j^{0}=7 .3 \times1 0^{-8} \mathrm{A / c m}^{2}
$$
G. $$
j^{0}=2 .5 \times1 0^{-6} \mathrm{A / c m}^{2}
$$
H. $$
j^{0}=1. 9 \times1 0^{-5} \mathrm{A / c m}^{2}
$$
I. $$
j^{0}=8 .8 \times1 0^{-2} \mathrm{A / c m}^{2}
$$
J. $$
j^{0}=4 .8 \times1 0^{-5} \mathrm{A / c m}^{2}
$$
Answer: H
Electrolyzing a 0.5 mol/L $H_{\mathrm{2}}SO_{\mathrm{4}}$ aqueous solution using nickel as the cathode at 20°C, when the electrode potential is -0.479 V, what are the cathodic current density and the hydrogen evolution overpotential? It is known that the $a$ value for hydrogen evolution on nickel is 0.63 $\mathrm{V}$, and the $b$ value is 0.11 $\mathbf{V}$ is().

Options:
A. $$
j=3. 2 4 A / c m^{2}
$$
B. $$
j=0. 4 5 A / c m^{2}
$$
C. $$
j=2. 1 1 A / c m^{2}
$$
D. $$
j=1. 5 8 A / c m^{2}
$$
E. $$
j=5. 5 5 A / c m^{2}
$$
F. $$
j=0. 2 0 A / c m^{2}
$$
G. $$
j=4. 6 9 A / c m^{2}
$$
H. $$
j=0. 0 1 6 A / c m^{2}
$$
I. $$
j=1. 0 0 A / c m^{2}
$$
J. $$
j=0. 3 3 A / c m^{2}
$$
Answer: H
Use the relative motion of the Andromeda and Milky Way galaxies to estimate their total mass for the case $h=0. 5$ . What is the corresponding mass-to-light ratio of these galaxies?

Options:
A. $$
M / L_{B}=4 4 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
B. $$
M / L_{B}=4 8 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
C. $$
M / L_{B}=4 2 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
D. $$
M / L_{B}=6 4 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
E. $$
M / L_{B}=5 8 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
F. $$
M / L_{B}=6 0 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
G. $$
M / L_{B}=5 0 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
H. $$
M / L_{B}=3 6 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
I. $$
M / L_{B}=4 0 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
J. $$
M / L_{B}=5 2 \, \mathrm{M}_{\odot} / L_{\odot}.
$$
Answer: B
The gaseous ring orbiting the central galaxies of the M96 group has an orbital period of $4. 1 \times1 0^{9}$ years.
What is the combined mass (in $\mathbf{M}_{\odot}$ ) of the two galaxies?

Options:
A. $$
4. 8 9 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
B. $$
6. 1 9 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
C. $$
4. 7 3 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
D. $$
5. 9 6 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
E. $$
5. 3 8 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
F. $$
5. 1 4 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
G. $$
6. 3 8 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
H. $$
6. 5 2 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
I. $$
4. 2 7 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
J. $$
5. 7 7 \times1 0^{1 1} \, \mathrm{M}_{\odot}
$$
Answer: E
If the iron ions in hard water exceed _______, they combine with tea polyphenols, causing the tea to turn dark brown, with a layer of iron film floating on the surface, also known as "rust oil," resulting in an astringent taste, making it undrinkable.

Options:
A. 0.10%
B. 0.15%
C. 0.25%
D. 0.05%
E. 1.00%
F. 2.00%
G. 0.50%
H. 0.01%
I. 5.00%
J. 10.0%
Answer: D
The inertia of the rigid body is $\hat{I}=\left( \begin{matrix} {{{1 5 0}}} & {{{0}}} & {{{-1 0 0}}} \\ {{{0}}} & {{{2 5 0}}} & {{{0}}} \\ {{{-1 0 0}}} & {{{0}}} & {{{3 0 0}}} \\ \end{matrix} \right) \mathrm{kg} \cdot \mathrm{m}^{2}$, and the center of mass is at the origin. If it rotates with an angular velocity $1 0 \boldsymbol{e}_{x}+0 \boldsymbol{e}_{y}+0 \boldsymbol{e}_{z}$, the external torque is ().

Options:
A. $$
4 0 0 0 0 e_{z} ( \mathrm{N} \cdot\mathrm{m} )
$$
B. $$
0 0 0 5 0 e_{y} ( \mathrm{N} \cdot\mathrm{m} )
$$
C. $$
1 0 0 1 0 e_{z} ( \mathrm{N} \cdot\mathrm{m} )
$$
D. $$
1 0 0 0 0 e_{y} ( \mathrm{N} \cdot\mathrm{m} )
$$
E. $$
2 0 0 0 0 e_{y} ( \mathrm{N} \cdot\mathrm{m} )
$$
F. $$
1 1 0 0 0 e_{z} ( \mathrm{N} \cdot\mathrm{m} )
$$
G. $$
0 0 2 0 0 e_{x} ( \mathrm{N} \cdot\mathrm{m} )
$$
H. $$
0 0 1 5 0 e_{z} ( \mathrm{N} \cdot\mathrm{m} )
$$
I. $$
3 0 0 0 0 e_{x} ( \mathrm{N} \cdot\mathrm{m} )
$$
J. $$
0 5 0 0 0 e_{x} ( \mathrm{N} \cdot\mathrm{m} )
$$
Answer: D
Two particles undergo an elastic collision. Their masses are $m_{1}$ and $m_{2}$, with initial velocities $u_{1}$ and $\alpha u_{1}$, respectively. If the initial kinetic energies of the two particles are the same and the first particle comes to rest after the collision, what is the value of $a$?

Options:
A. $$
\alpha=0 \pm\sqrt{4} \;
$$
B. $$
\alpha=1.5 \pm\sqrt{2} \;
$$
C. $$
\alpha=1 \pm\sqrt{2.5} \;
$$
D. $$
\alpha=-1 \pm\sqrt{1} \;
$$
E. $$
\alpha=-1 \pm\sqrt{2} \;
$$
F. $$
\alpha=0.5 \pm\sqrt{5} \;
$$
G. $$
\alpha=-2 \pm\sqrt{1} \;
$$
H. $$
\alpha=0.5 \pm\sqrt{3} \;
$$
I. $$
\alpha=1 \pm\sqrt{3} \;
$$
J. $$
\alpha=2 \pm\sqrt{0.5} \;
$$
Answer: E
In the $K^{\prime}$ system, a light beam is emitted in a direction at an angle $\theta_{0}$ with the $x^{\prime}$ axis. In the $K$ system, what is the angle $\theta$ that the light beam makes with the $x$ axis? (The $K^{\prime}$ system is moving relative to the $K$ system at a speed $v$ along the $x$ axis).

Options:
A. $$
\frac{c \operatorname{tan} \theta_{0}-v} {c+v \operatorname{c o s} \theta_{0}}
$$
B. $$
\frac{c \operatorname{c o s} \theta_{0}+v} {c-v \operatorname{c o s} \theta_{0}}
$$
C. $$
\frac{c \operatorname{sin} \theta_{0}+v} {c+v \operatorname{sin} \theta_{0}}
$$
D. $$
\frac{v \operatorname{cos} \theta_{0}+c} {c+v \operatorname{tan} \theta_{0}}
$$
E. $$
\frac{c \operatorname{tan} \theta_{0}+v} {c+v \operatorname{tan} \theta_{0}}
$$
F. $$
\frac{c \operatorname{c o s} \theta_{0}+v} {c+v \operatorname{c o s} \theta_{0}}
$$
G. $$
\frac{c \operatorname{c o s} \theta_{0}+v} {v+c \operatorname{sin} \theta_{0}}
$$
H. $$
\frac{v \operatorname{c o s} \theta_{0}+c} {v+c \operatorname{c o s} \theta_{0}}
$$
I. $$
\frac{c \operatorname{sin} \theta_{0}+v} {c-v \operatorname{c o s} \theta_{0}}
$$
J. $$
\frac{c \operatorname{c o s} \theta_{0}-v} {c-v \operatorname{c o s} \theta_{0}}
$$
Answer: F
When a train travels on a railroad, it experiences a jolt every time it passes a junction, causing the carriage to oscillate up and down on the springs. Assuming each section of the track is 12.5m long, each spring on the carriage bears a weight of 0.50t, and each spring compresses 10mm under a force of 1.0t. If the weight of the spring itself is negligible, at what speed does the train travel to achieve the maximum amplitude of the spring's oscillation?

Options:
A. $$
12 12 ( \mathrm{m / s} )
$$
B. $$
6 6 ( \mathrm{m / s} )
$$
C. $$
20 20 ( \mathrm{m / s} )
$$
D. $$
11 11 ( \mathrm{m / s} )
$$
E. $$
9 9 ( \mathrm{m / s} )
$$
F. $$
18 18 ( \mathrm{m / s} )
$$
G. $$
8 8 ( \mathrm{m / s} )
$$
H. $$
14 14 ( \mathrm{m / s} )
$$
I. $$
10 10 ( \mathrm{m / s} )
$$
J. $$
15 15 ( \mathrm{m / s} )
$$
Answer: G
To assume $f \! \in\! L ( [ 0, 1 ] )$, and $\int_{0}^{1} \! f ( x ) \mathrm{d} x \!=\! 1$. What is the value of $I$?

Options:
A. $\frac16 - \frac{1}{2\pi}$
B. $e^{-1}$
C. $\frac{1}{e}$
D. $\frac13$
E. $\frac16$
F. $\frac{\pi}{6}$
G. $\frac{7}{12}$
H. $\frac12$
I. $\frac{2}{5}$
J. $ln2$
Answer: E
A separately excited DC motor has the following nameplate data: $\mathrm{P}_{\mathrm{N}}=13 \mathrm{kW}, \ \ \mathrm{U}_{\mathrm{N}}=220 \mathrm{V}, \ \ \mathrm{I}_{\mathrm{N}}=68.6 \mathrm{A}, \ \ \mathrm{n}_{\mathrm{N}}=1500 \mathrm{r}/\mathrm{min}$. When lifting heavy objects with a load torque of $\mathrm{T_{z}={\frac{1} {2}} T_{N}}$, and operating on its inherent characteristics, the armature reversal method is used for braking. If the instantaneous current at the start of braking should not exceed $2 \mathrm{I_{N}}$, how much resistance should be connected in series in the armature circuit?

Options:
A. 3.872Ω
B. 4.150Ω
C. 4.600Ω
D. 2.475Ω
E. 4.320Ω
F. 3.756Ω
G. 1.987Ω
H. 3.211Ω
I. 2.894Ω
J. 2.560Ω
Answer: I
A wound rotor induction motor is given with $\mathrm{P}_{\mathrm{N}}=44 \, \mathrm{kW}, \; \mathrm{n}_{\mathrm{N}}=1435 \, \mathrm{r/min}, \; \mathrm{E}_{\mathrm{2N}}=243 \, \mathrm{V}, \; \mathrm{I}_{\mathrm{2N}}=110 \, \mathrm{V}$. Assuming the load torque during startup is $\mathrm{T_{z}=0.8 T_{N}}$, the maximum allowable starting torque is $\mathbf{T}_{\mathrm{st1}}=1.87 \, \mathbf{T}_{\mathrm{N}}$, and the switching torque is $\mathbf{T}_{\mathrm{st2}}=\mathbf{T}_{\mathrm{N}}$, The resistance value for each segment using an analytical method is ().

Options:
A. 0.051Ω,0.091Ω,0.171Ω,0.317Ω,0.591Ω
B. 0.050Ω,0.090Ω,0.170Ω,0.320Ω,0.590Ω
C. 0.045Ω,0.085Ω,0.160Ω,0.310Ω,0.580Ω
D. 0.052Ω,0.092Ω,0.172Ω,0.318Ω,0.592Ω
E. 0.046Ω,0.086Ω,0.162Ω,0.311Ω,0.582Ω
F. 0.053Ω,0.093Ω,0.173Ω,0.319Ω,0.593Ω
G. 0.048Ω,0.089Ω,0.167Ω,0.313Ω,0.585Ω
H. 0.044Ω,0.084Ω,0.159Ω,0.309Ω,0.579Ω
I. 0.049Ω,0.088Ω,0.165Ω,0.315Ω,0.586Ω
Answer: G
Air at 20°C and 101.3 kPa flows over a flat plate at a speed of 15 m/s. At $R_e{x} = 1.0 \times 10^{5}$, find the velocity gradient at the wall.

Options:
A. $$
= 1 5 4 2 3 \; \mathrm{s}^{-1}
$$
B. $$
= 1 5 8 6 1 \; \mathrm{s}^{-1}
$$
C. $$
= 1 6 1 8 0 \; \mathrm{s}^{-1}
$$
D. $$
= 1 3 9 9 7 \; \mathrm{s}^{-1}
$$
E. $$
= 1 5 0 9 5 \; \mathrm{s}^{-1}
$$
F. $$
= 1 5 2 4 0 \; \mathrm{s}^{-1}
$$
G. $$
= 1 4 9 3 2 \; \mathrm{s}^{-1}
$$
H. $$
= 1 7 5 6 8 \; \mathrm{s}^{-1}
$$
I. $$
= 1 4 7 8 0 \; \mathrm{s}^{-1}
$$
J. $$
= 1 6 2 3 5 \; \mathrm{s}^{-1}
$$
Answer: F
In a large room with a room temperature of 10 °C, there is a chimney with a diameter of 15 cm. Its vertical section is 1.5 m high and the horizontal section is $1 5 \mathrm{m}$ long. The average wall temperature of the chimney is $1 1 0 ^{\circ} \mathbb{C}$. What is the convective heat dissipation per hour ?

Options:
A. $$
= 4 8 9 2. 7 \quad\mathrm{W}
$$
B. $$
= 4 9 3 8. 5 \quad\mathrm{W}
$$
C. $$
= 5 0 3 4. 1 \quad\mathrm{W}
$$
D. $$
= 5 7 0 4. 9 \quad\mathrm{W}
$$
E. $$
= 5 8 9 1. 0 \quad\mathrm{W}
$$
F. $$
5 1 2 1. 4 \quad\mathrm{W}
$$
G. $$
= 4 3 7 6. 2 \quad\mathrm{W}
$$
H. $$
= 5 2 8 9. 6 \quad\mathrm{W}
$$
I. $$
= 6 1 2 0. 3 \quad\mathrm{W}
$$
J. $$
= 5 4 6 7. 8 \quad\mathrm{W}
$$
Answer: F
What are the three levels of mesh size that breeding net cages can be woven into?

Options:
A. 1.7 cm, 2.2 cm, 3.8 cm
B. 1.6 cm, 2 cm, 3.3 cm
C. 1.4 cm, 2.3 cm, 3.2 cm
D. 0.9 cm, 1.9 cm, 3.7 cm
E. 1.2 cm, 2 cm, 3 cm
F. 1.3 cm, 2 cm, 2.8 cm
G. 0.8 cm, 1.8 cm, 3.5 cm
H. 1.1 cm, 2.1 cm, 3.6 cm
I. 1.5 cm, 2.5 cm, 4 cm
J. 1 cm, 2 cm, 2.5 cm
Answer: E
A plane electromagnetic wave is incident perpendicularly on a metal surface. Prove that the energy of the electromagnetic wave penetrating into the metal is entirely converted into Joule heat.

Options:
A. $$
\langle S \rangle=\langle P \rangle/2
$$
B. $$
\langle Q \rangle=\langle S \rangle
$$
C. $$
\langle S \rangle<\langle P \rangle
$$
D. $$
\langle S \rangle+\langle P \rangle=0
$$
E. $$
\langle S \rangle>\langle P \rangle
$$
F. $$
\langle S \rangle=\langle P \rangle
$$
G. $$
\langle R \rangle=\langle P \rangle
$$
H. $$
\langle T \rangle=\langle P \rangle
$$
I. $$
\langle S \rangle\neq\langle P \rangle
$$
J. $$
\langle S \rangle=\langle Q \rangle
$$
Answer: F
Which category of movement structure does football belong to?

Options:
A. Variant Combination
B. Sequential Patterns
C. Integrated Dynamics
D. Structured Convergence
E. Static Modification
F. Fixed Synchronization
Answer: A
Suppose that a ball of mass $m$ "mswmum
$$
\mathbf{v}=v_{x} \mathbf{\hat{i}}+v_{y} \mathbf{\hat{j}}+v_{z} \mathbf{\hat{k}},
$$
where $\hat{\mathbf{i}}, \hat{\mathbf{j}},$ and $\hat{\mathbf{k}}$ are unit vectors pointing directly east, north, and upward, respectively, at the point where the ball is thrown. The latitude of the ball is $L$ when it is thrown.
(a) Show that the components of the Coriolis force on the ball are given by
$$
\mathbf{F}_{C}=-2 m \omega[ ( v_{z} \operatorname{c o s} L-v_{y} \operatorname{s i n} L ) \hat{\mathbf{i}}+v_{x} \operatorname{s i n} L \hat{\mathbf{j}}-v_{x} \operatorname{c o s} L \hat{\mathbf{k}} ].
$$
Hint: Be sure to represent the components of the vector $\omega$ in terms of the coordinate system on the surface of Earth defined by $\hat{\mathbf{i}}, \hat{\mathbf{j}},$ and $\mathbf{\hat{k}}$ , with the origin of the system at the position where the ball was thrown.

Options:
A. $$
-\left( 2. 7 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}+\left( 3. 4 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf i}}.
$$
B. $$
-\left( 3. 0 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}+\left( 2. 6 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}.
$$
C. $$
-\left( 2. 2 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf i}}+\left( 3. 9 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}.
$$
D. $$
-\left( 2. 6 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}+\left( 3. 5 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf i}}.
$$
E. $$
-\left( 2. 9 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf i}}+\left( 3. 2 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}.
$$
F. $$
-\left( 2. 8 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}+\left( 3. 3 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}.
$$
G. $$
-\left( 2. 3 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}+\left( 3. 8 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}.
$$
H. $$
-\left( 2. 4 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}+\left( 3. 7 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}.
$$
I. $$
-\left( 2. 1 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf k}}+\left( 4. 0 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}.
$$
J. $$
-\left( 2. 5 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf i}}+\left( 3. 6 \mathrm{~ m m ~ s^{-2} ~} \right) \hat{{\bf j}}.
$$
Answer: F
The present-day Hill radius of Jupiter. Express your answer in terms of the radius of Jupiter, as well as in astronomical units is().

Options:
A. $$
4 4 4 4 \ R_{J}
$$
B. $$
1 0 0 0 \ R_{J}
$$
C. $$
2 2 2 2 \ R_{J}
$$
D. $$
3 3 3 3 \ R_{J}
$$
E. $$
7 7 7 7 \ R_{J}
$$
F. $$
8 9 9 9 \ R_{J}
$$
G. $$
6 6 6 6 \ R_{J}
$$
H. $$
9 8 8 8 \ R_{J}
$$
I. $$
5 5 5 5 \ R_{J}
$$
J. $$
2 3 4 5 \ R_{J}
$$
Answer: B
Above an infinite conducting plane, two types of dielectric materials are symmetrically placed on the left and right, with dielectric constants $\varepsilon_{1}$ and $\varepsilon_{2}$, respectively. In the first dielectric medium, at a point located a distance $a$ from the conducting plane and a distance $b$ from the dielectric interface, a point charge $q$ is placed. If the region of interest is the space within the first medium, what is the value of the image charge?

Options:
A. $$
q^{\prime}={\frac{\varepsilon_{1}+\varepsilon_{2}} {2\varepsilon_{1}-\varepsilon_{2}}} q
$$
B. $$
q^{\prime}={\frac{2\varepsilon_{1}-\varepsilon_{2}} {\varepsilon_{1}+\varepsilon_{2}}} q
$$
C. $$
q^{\prime}={\frac{\varepsilon_{1}\varepsilon_{2}} {\varepsilon_{1}+\varepsilon_{2}}} q
$$
D. $$
q^{\prime}={\frac{\varepsilon_{1}-2\varepsilon_{2}} {\varepsilon_{1}+\varepsilon_{2}}} q
$$
E. $$
q^{\prime}={\frac{\varepsilon_{1}+2\varepsilon_{2}} {\varepsilon_{1}-\varepsilon_{2}}} q
$$
F. $$
q^{\prime}={\frac{\varepsilon_{1}+\varepsilon_{2}} {\varepsilon_{1}-\varepsilon_{2}}} q
$$
G. $$
q^{\prime}={\frac{\varepsilon_{1}-\varepsilon_{2}} {\varepsilon+\varepsilon_{2}}} q
$$
H. $$
q^{\prime}={\frac{\varepsilon_{1}-2\varepsilon_{2}} {2\varepsilon_{1}+\varepsilon_{2}}} q
$$
I. $$
q^{\prime}={\frac{\varepsilon_{1}-\varepsilon_{2}} {\varepsilon_{1}+2\varepsilon_{2}}} q
$$
J. $$
q^{\prime}={\frac{\varepsilon_{2}-\varepsilon_{1}} {\varepsilon_{1}+\varepsilon_{2}}} q
$$
Answer: G
In the magnetic field generated by the current in a long straight conductor placed along the $z$-axis (the integration path must not encircle the current), what are the vector potential difference and scalar potential difference between the point $(0, 1, 0)$ and the point $(0, -1, 0)$?

Options:
A. Vector magnetic potential difference: $\pm{\frac{I} {2}}$
Scalar magnetic potential difference: $\Delta\varphi_{m}=0$
B. Vector magnetic potential difference: $\pm{\frac{I} {3}}$
Scalar magnetic potential difference: $\Delta\varphi_{m}=\pm I$
C. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}=\pm{\frac{I} {2}}$
D. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}=-{\frac{I} {\mu}}$
E. Vector magnetic potential difference: $-\frac{I} {4}$
Scalar magnetic potential difference: $\Delta\varphi_{m}=0$
F. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}={\frac{I\mu} {2}}$
G. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}=\pm{\frac{I^{2}} {2}}$
H. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}=\pm{\frac{\mu I} {2}}$
I. Vector magnetic potential difference: $\frac{I} {\pi}$
Scalar magnetic potential difference: $\Delta\varphi_{m}=0$
J. Vector magnetic potential difference: 0
Scalar magnetic potential difference: $\Delta\varphi_{m}=\pm{\frac{2I} {3}}$
Answer: C
A wire is tightly wound into a circular loop with a total of 100 turns. The radius of the loop is 5 cm. When the loop rotates about its vertical diameter at a speed of $500 \, \operatorname{r} / \operatorname{min}$, the measured terminal voltage of the wire is 1.5 mV (RMS). What is the horizontal component of the Earth's magnetic field induction?

Options:
A. $$
4. 6 5 \times1 0^{-5} \mathrm{T}
$$
B. $$
5. 7 3 \times1 0^{-5} \mathrm{T}
$$
C. $$
4. 9 8 \times1 0^{-5} \mathrm{T}
$$
D. $$
6. 1 4 \times1 0^{-5} \mathrm{T}
$$
E. $$
5. 4 9 \times1 0^{-5} \mathrm{T}
$$
F. $$
4. 7 2 \times1 0^{-5} \mathrm{T}
$$
G. $$
6. 0 9 \times1 0^{-5} \mathrm{T}
$$
H. $$
5. 8 0 \times1 0^{-5} \mathrm{T}
$$
I. $$
5. 2 3 \times1 0^{-5} \mathrm{T}
$$
J. $$
5. 1 6 \times1 0^{-5} \mathrm{T}
$$
Answer: J
Given the magnetic field intensity of a uniform plane wave propagating in free space is
$$
H \,=\, \Big( e_{x} \, \frac{3} {2} \,+\, e_{y} \,+\, e_{z} \Big) \, 10^{-6} \operatorname{cos} \Big[ \, \omega t \,-\pi\Big(-\, x \,+\, y \,+\, \frac{1} {2} z \Big) \, \Big] \quad\mathrm{A / m},
$$
find the propagation direction of the wave.

Options:
A. $$
e_{x} \ \frac{1} {2}+e_{y} \ \frac{1} {3}+e_{z} \ \frac{2} {3}
$$
B. $$
-\ e_{x} \ \frac{1} {3}+e_{y} \ \frac{1} {3}-e_{z} \ \frac{1} {3}
$$
C. $$
-\ e_{x} \ \frac{1} {2}+e_{y} \ \frac{1} {2}-e_{z} \ \frac{2} {3}
$$
D. $$
\ e_{x} \ \frac{1} {2}- e_{y} \ \frac{2} {3}+ e_{z} \ \frac{2} {3}
$$
E. $$
e_{x} \ \frac{2} {3} - e_{y} \ \frac{1} {2} - e_{z} \ \frac{1} {3}
$$
F. $$
e_{x} \ \frac{2} {3} + e_{y} \ \frac{1} {3} - e_{z} \ \frac{2} {3}
$$
G. $$
-\ e_{x} \ \frac{2} {3}+e_{y} \ \frac{2} {3}+e_{z} \ \frac{1} {3}
$$
H. $$
-\ e_{x} \ \frac{2} {3}-e_{y} \ \frac{1} {3}+e_{z} \ \frac{1} {3}
$$
I. $$
-\ e_{x} \ \frac{1} {3}-e_{y} \ \frac{1} {2}+e_{z} \ \frac{1} {3}
$$
J. $$
e_{x} \ \frac{1} {3} - e_{y} \ \frac{2} {3} + e_{z} \ \frac{2} {3}
$$
Answer: G
In the complex liquid-phase reaction
$$
(a), \mathrm{A + B \longrightarrow P};
(b), \mathrm{A + P \longrightarrow S}.
$$
The initial concentrations of the reactants are $c_{\mathrm{A \, 0}} \!=\! 2.0 \, \mathrm{mol/L}$, $c_{\mathrm{B \, 0}} \!=\! 4.0 \, \mathrm{mol/L}$, and $c_{\mathrm{P \, 0}} \!=\! c_{\mathrm{S \, 0}} \!=\! 0$. In the batch reactor, measurements show that $c_{\mathrm{A}} \!=\! 0.3 \, \mathrm{mol/L}$ and $c_{\mathrm{B}} \!=\! 2.4 \, \mathrm{mol/L}$. What is the yield of product $\mathrm{P}$?

Options:
A. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{0. 9} {4. 0}} \!=\! 0. 2 2 5
$$
B. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 5} {4. 0}} \!=\! 0. 3 7 5
$$
C. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{2. 0} {4. 0}} \!=\! 0. 5 0 0
$$
D. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 8} {4. 0}} \!=\! 0. 4 5 0
$$
E. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 6} {4. 0}} \!=\! 0. 4 0 0
$$
F. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 4} {4. 0}} \!=\! 0. 3 5 0
$$
G. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 3} {4. 0}} \!=\! 0. 3 2 5
$$
H. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{0. 7} {4. 0}} \!=\! 0. 1 7 5
$$
I. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 2} {4. 0}} \!=\! 0. 3 0 0
$$
J. $$
\phi\!=\! {\frac{c_{\mathrm{P}}} {c_{\mathrm{B 0}}}} \!=\! {\frac{1. 0} {4. 0}} \!=\! 0. 2 5 0
$$
Answer: B
In the butyl acetate production workshop, a batch reactor is used, operating at a temperature of 100°C. Each batch is charged with 1 kmol of acetic acid and 4.96 kmol of n-butanol, with the addition of 0.032% sulfuric acid (based on the total feed) as a catalyst. The reaction rate, based on acetic acid, is given as:
$$
(-r_{\mathrm{A}}) = 1.045 c_{\mathrm{A}}^2 \ \mathrm{kmol} / (\mathrm{m}^3 \cdot \mathrm{h})
$$
The densities of acetic acid and n-butanol are known to be $960\ \mathrm{kg}/\mathrm{m}^3$ and $740\ \mathrm{kg}/\mathrm{m}^3$, respectively. Calculate the reaction time required for acetic acid conversion rates ($x_{\mathrm{A}}$) of 0.5, 0.9, and 0.99, respectively is ().

Options:
A. 0.520h,4.25h,53.5h
B. 0.560h,4.75h,54.8h
C. 0.450h,3.50h,48.3h
D. 0.600h,4.50h,60.0h
E. 0.470h,3.80h,49.6h
F. 0.490h,4.40h,52.0h
G. 0.535h,4.18h,52.9h
H. 0.495h,4.30h,51.7h
I. 0.510h,4.00h,50.8h
J. 0.580h,4.10h,55.2h
Answer: G
The rate equation for the liquid-phase autocatalytic reaction A + P → P + P is expressed as:
$$(-r_{\mathrm{A}})=-\frac{\mathrm{d}c_{\mathrm{A}}}{\mathrm{d}t}=kc_{\mathrm{A}}c_{\mathrm{P}}\quad\mathrm{mol/(L\cdot h)}$$
The reaction rate is measured in an isothermal batch reactor, where $c_{A0} = 0.95$ mol/L, $c_{\mathrm{m}} = 0.05$ mol/L. After 1 hour, the maximum reaction rate can be determined. What is the reaction rate constant $k$ at this temperature?

Options:
A. $$
2. 9 4 4 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
B. $$
3. 0 9 8 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
C. $$
2. 6 4 9 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
D. $$
3. 0 5 4 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
E. $$
3. 2 2 0 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
F. $$
2. 7 5 0 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
G. $$
2. 8 7 3 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
H. $$
3. 1 8 6 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
I. $$
2. 6 7 5 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
J. $$
2. 8 1 2 \mathrm{~ L / ( m o l ~ \cdot~ h )}
$$
Answer: A
In a batch reactor, the following reactions take place:
$$
\text{A} + \text{B} \rightarrow \text{P} + \text{S}\\\text{A} + \text{C} \rightarrow \text{R} + \text{M}
$$
It is known that:
$$
r_{\mathrm{P}}=k_{1} c_{\mathrm{A}} c_{\mathrm{B}}
$$
$$
r_{R}=k_{2} c_{\mathrm{A}} c_{\mathrm{C}}
\\k_{1} =1.5\times10^{-3}L/(mol·min)
\\k_{2} =1.8\times10^{-3}L/(mol·min)
$$
$$
c_{\mathrm{A 0}} \!=\! 1.3 \ \mathrm{mol/L}
$$
$$
c_{\mathrm{B 0}}=2.2 \ \mathrm{mol/L}
$$
$$
c_{\mathrm{C 0}}=\! 2 \! \ \mathrm{mol/L}
$$
$$
c_{\mathrm{P 0}}=c_{\mathrm{S 0}}=c_{\mathrm{R 0}}=c_{\mathrm{M 0}}=0
$$
When the yield of $\mathbf{P}$ is 0.3 (based on $\text{A}$), what are the conversion rate of reactant $\text{A}$ ($x_{\mathrm{A}}$) and the yield of product $\mathbf{R}$?

Options:
A. $$
\phi_{R}=0.250
\\x_{A}=0.700
$$
B. $$
\phi_{R}=0.300
\\x_{A}=0.640
$$
C. $$
\phi_{R}=0.270
\\x_{A}=0.590
$$
D. $$
\phi_{R}=0.295
\\x_{A}=0.650
$$
E. $$
\phi_{R}=0.340
\\x_{A}=0.610
$$
F. $$
\phi_{R}=0.310
\\x_{A}=0.580
$$
G. $$
\phi_{R}=0.290
\\x_{A}=0.600
$$
H. $$
\phi_{R}=0.283
\\x_{A}=0.630
$$
I. $$
\phi_{R}=0.321
\\x_{A}=0.622
$$
J. $$
\phi_{R}=0.315
\\x_{A}=0.560
$$
Answer: I
At 650°C, the decomposition reaction of phosphine is an irreversible first-order reaction, expressed as:
$$
4 \mathrm{PH}_{3} ( g ) \longrightarrow \mathrm{P}_{4} ( g ) + 6 \mathrm{H}_{2} ( g )
$$
The rate constant is given by the equation:
$$
\log k = -\frac{18963}{T} + 2 \log T + 12.13
$$
Here, the unit of $k$ is $1 / \mathrm{s}$, and $T$ represents the absolute temperature.
The reaction is carried out in an isothermal process at 650°C within a constant-volume reactor. The feedstock contains only $\mathrm{PH}_{3}$, and the pressure $p$ is 0.10133 MPa.
If the decomposition of phosphine takes place in a plug flow reactor under the conditions of 0.10133 MPa, 650°C, and a residence time of 500 s, what is the conversion rate?

Options:
A. 0.815
B. 0.812
C. 0.775
D. 0.800
E. 0.828
F. 0.821
G. 0.794
H. 0.789
I. 0.770
J. 0.806
Answer: J