Question

Fluid Mechanics:

1) A fluid flow enters a plane-wall diffuser that has an entrance area of Ao at a velocity Uo. Uo Ao (a) Assuming the fluid is inviscid, determine the velocity gradient dU/dx in terms of Uo and Ao for a value of ф-0° and ф-20%. (b) Assuming a real viscous fluid, what is the effect of the boundary layers on the pressure gradient? In which assumption (inviscid or viscous) will the exit pressure be highest? Explain your answer.

Answer 1

Here option the entrance diameter diffusing of the we know that = pi O^2 0/4 D_0 = squareroot A_0/[1/4 pi] Here, is the diameter at the entrance of the difference the obtain the expression for inroad diameter of the diffuser. we know that = D = D_0 + 2 times tan phi when phi = 20 degree, the cross suction area increase calculate the increases are of the diffusing A = 1/4 pi D^2 hence substitute [D_0 + 2x tan phi] for 0 A = 1/4 [D_0 + 2x + an phi]^2 = 1/4 pi [squareroot 4 A_0/pi + 2x + an phi]^2 \r\n Then obtain the expression for velocity using Continuity equation. A_u = A_0 u_0 u = A_0 u_0/A Substitute 1/4 pi [squareroot 4 A_0/pi + 2x + tan phi]^2 for A u = A_0 u_0/1/4 pi [squareroot 4 A_0/pi + 2x + 3 tan phi]^2 = 4 A_0 u_0/pi [squareroot 4 A_0/pi + 2