A pipe has a porous section of length L as shown in the figure. Velocity at the start of this section of V0. If fluid leaks into the pipe through the porous section at a volumetric rate per unit area q(x/L)2, what will be axial velocity in the pipe at any „x‟? Assume incompressible one dimensional flow i.e., no gradients in the radial direction ?

Related Mcqs:

1. Bernoulli’s equation for fluid flow is derived following certain assumptions. Out of the assumptions listed below, which set of assumptions is used in derivation of Bernoulli’s equation? A. Fluid flow is frictionless & irrotational. B. Fluid flow is steady. C. Fluid flow is uniform & turbulent. D. Fluid is compressible. E. Fluid is incompressible ?

   A. A, C, D
   B. B, D, E
   C. A, B, E
   D. A, D, E

2. The pressure drop per unit length of pipe incurred by a fluid ‘X’ flowing through pipe is Δp. If another fluid ‘Y’ having both the specific gravity & density just double of that of fluid ‘X’, flows through the same pipe at the same flow rate/average velocity, then the pressure drop in this case will be__________________?

   A. Δp
   B. 2Δp
   C. Δp2
   D. Δp/2

3. In a fully turbulent flow (Re > 105) in a pipe of diameter ‘d’, for a constant pressure gradient, the dependence of volumetric flow rate of an incompressible fluid is_______________?

   A. d
   B. d2
   C. d2.5
   D. d4

4. For turbulent flow of an incompressible fluid through a pipe, the flow rate „Q‟ is proportional to (Δ P)n, where ΔP is the pressure drop. The value of exponent ‘n’ is_________________?

   A. 1
   B. 0
   C. < 1
   D. > 1

5. For the laminar flow of a fluid in a circular pipe of radius R, the Hagen-Poisseule equation predicts the volumetric flow rate to be proportional to____________________?

   A. R
   B. R2
   C. R4
   D. R0.5

6. For laminar flow of Newtonian fluids through a circular pipe, for a given pressure drop and length & diameter of pipe, the velocity of fluid is proportional to (where, μ = fluid viscosity ) ?

   A. μ
   B. 1/μ
   C. √μ
   D. 1/√μ

7. Mach number is defined as the ratio of the local flow velocity to the sonic velocity in the fluid. For what value of Mach number, the gases are considered incompressible ?

   A. < 0.3
   B. > 3
   C. 50
   D. 1

8. In case of turbulent flow of a Newtonian fluid in a straight pipe, the maximum velocity is equal to (where, Vavg = average fluid velocity)?

   A. Vavg
   B. 1.2 Vavg
   C. 1.5 Vavg
   D. 1.8 Vavg

9. The ratio of average fluid velocity to the maximum velocity in case of laminar flow of a Newtonian fluid in a circular pipe is_____________________?

   A. 0.5
   B. 1
   C. 2
   D. 0.66

10. What is the ratio of the velocity at the axis of the pipe to the mean velocity of flow in case of pipe flow under viscous condition ?

    A. 0.5
    B. 0.67
    C. 1
    D. 2