Patent GB-1462865-A (GB)
Title: Fluid flow simulation appratus
IPC: G06G7/57
Filed: 1973-05-24
Abstract: 1462865 Simulating fluid flow BRITISH AIRCRAFT CORP Ltd 7 May 1974 [24 May 1973] 24846/73 Heading G4G A two-terminal network for simulating flow of water through a pipe (a pipe cell) comprises a function generator responsive to an input voltage E for generating an output voltage y = E-aE<SP>1</SP><SP>/n</SP> where a and n are constants, and n lies between 1À80 and 2À00, and wherein a bypass resistance is connected between one input terminal and the output of the function generator whereby the simulated hydraulic resistance may be varied. The invention is presented as a development of the pipe cell of Specification 1,068,824 in which a network of resistors and biased diodes provides a characteristic defined approximately by E = ki<SP>n</SP>. When n has a value 1À85, the voltage E may represent fluid head, and i flow rate, whilst k represents the hydraulic resistance of the pipe. In order to permit variation of k, a unity-gain amplifier is added to the circuit in such a manner that it receives an input voltage E-iR 1 , where R 1  is the resistance of the first resistor of the circuit. A by-pass resistance R L  is then connected between the output of the amplifier and the input terminal of the circuit and a wide variation of k may be obtained by varying R L . It is shown in the Specification that the output voltage of the amplifier may be written E-aE<SP>1/n</SP> where a is a constant. According to the invention, this function may be represented for a value a= 0À600 and n=1À85 by the three-segment piecewise linear approximation OABC, Fig. 2, and the circuit of Fig. 3 simulates this characteristic. A voltage E is fed through a buffer A1 to an operational amplifier A2 having alternative parallel input paths Z 1 , R 3  and D 1 , R 1 , the currents i 1 , i 2  through the paths being summed at the inverting input of A2 whereby the output of A2 is -R 2 (i 1 +i 2 ). The break point A occurs at the threshold of D 1  and the break point B at the threshold of Z 1 , the slopes AB and BC being determined by the resistances R 1 , R 2 . Thus, the output voltage of amplifier approximates -(E-aE<SP>1/n</SP>) and this voltage is inverted by amplifier A3. The cell circuit is completed by the bypass resistance R L . The cell current is given by: I=[E-(E-aE<SP>1/n</SP>)]/R L  or I = aE<SP>1/n</SP>/R L , so that which is the required fluid-flow equation with hydraulic resistance represented by the constant term. This may be adjusted by variation of R L . Operation of the cell for negative E is provided for by addition of diodes Z 2  and D 2 . Fig. 6 shows a suitable circuit for variable R L  incorporating wide and narrow ranges selected by a two-position range switch. Each range utilizes four resistors switched by binary logic to yield current values 0, i, 2i ... 15i in the wide range and values i/16 to 17i/16 in the narrow range, where i is the current passed by unit resistance r. Interpolation between discrete switchable values is obtained by the resistances r/2 and 8r. The Specification also describes (Fig. 4, not shown) Zener diode circuits for protecting the cell and the power supply from excess currents.