3.There is one mistake in the following calculation. Identifythe error, when it was first made.

Q4.) [Reynolds Transport Theorum] Water flows into a sluice gate at a uniform speed U, and the flow is steady. The channel is 2 metre wide and at position A, its depth Da is 4 metres. As shown in the diagram, the obstacle presented by the sluice gate causes a complex flow pattern downstream, with a counterflow at the surface. At position B, the total depth of the flow, De, is 2 metres, and the downstream horizontal flow speed varies with height x as given here: V(x) = K(1.5 – x) where K is a constant with a value of 1.8 s? Note that positive values refer to a downstream flow. Starting from the Reynolds Transport Theorum, and using mass as the quantity of interest, calculate U and also the total flow rate through the sluice gate. Uniform speed U 1 CONTROL VOLUME DA Vk6-5-) А B → Total mass Reynolds Transport Theorem for mass, M: bolestie el sdy) + fs(2.a) da of system doesn't change with time, :. O Maus 20 > Steady flow conditions mean (sav). :. We are left with [ → svladdA0 where dA: Wdon v(x)= K (1.5-6) :SWK 1.5-uda=0 ::SWK [15u - ale] =0 23 ;.3.69=0