Dimensional Analysis of Compound Section in The Regulate Section Channel Model for Maintenance Main Channel

Abstract A dimensionless number is used to express the relationship between parameters and is used to describe the research results. Commonly used dimensional analysis methods are the Basic Echelon method, the Buckingham method, the Rayleight method, the Stepwise method and the Langhaar method. The compound section in the regulated section channel model aims to make the section convenient to the flow existing discharge at tidal conditions, in sediment flushing. In this study using the Buckingham’s method of dimensional analysis to determine the weight equation for the flushing sediment (w) and the variables that have been scaled on the flume, W = • (B, B*, h, h*, ⊗h, t, V, Q, g, W,)w,) S ), where B is the width of the river (cm), B* is the width of the Flushing section (cm), h is the height of the water level (cm), h* is the height of the flushing section (cm), ®h is the difference in water level (cm), t is the tidal time period (s), V is the flow velocity (cm/s), Q is the water discharge (cm 3 /s), g is the gravity (cm/s 2 ), )S is the mass density of the sediment (gr/cm 3 ), )w is the density of the water mass (gr/cm 3 ). From the analysis results obtained equations = <?CDATA $\frac{{B}^{* }}{B}.\frac{{h}^{* }}{h}.\frac{\Delta h}{h}.\frac{v}{gt}.\frac{Q}{g{h}^{2}t}.{\rho }_{s}{h}^{3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> <mml:mi>B</mml:mi> </mml:mfrac> <mml:mo>.</mml:mo> <mml:mspace width="0.25" /> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>h</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> <mml:mi>h</mml:mi> </mml:mfrac> <mml:mo>.</mml:mo> <mml:mspace width="0.25" /> <mml:mfrac> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>h</mml:mi> </mml:mrow> <mml:mi>h</mml:mi> </mml:mfrac> <mml:mo>.</mml:mo> <mml:mspace width="0.25" /> <mml:mfrac> <mml:mi>v</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>.</mml:mo> <mml:mspace width="0.25" /> <mml:mfrac> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>.</mml:mo> <mml:mspace width="0.25" /> <mml:msub> <mml:mo>ρ</mml:mo> <mml:mi>s</mml:mi> </mml:msub> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> </mml:math> . Where w is the weight of the flushing sediment (gr), <?CDATA $\frac{{B}^{* }}{B}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> <mml:mi>B</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> is the ratio of the design cross-sectional width to the width of the estuary, <?CDATA $\frac{{h}^{* }}{h}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:msup> <mml:mi>h</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> <mml:mi>h</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> is the ratio of the flushing cross-sectional height to the water level, <?CDATA $\frac{\Delta h}{h}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>h</mml:mi> </mml:mrow> <mml:mi>h</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> is the ratio of the height water level to water depth, <?CDATA $\frac{v}{gt}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mi>v</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> is the velocity of falling sediment, <?CDATA $\frac{Q}{g{h}^{2}t}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> is the discharge of sediment flushing, ρ s h 3 is the hydrostatic pressure.