Fluid Mechanics GATE 2019, Set-2

• 1. A two-dimensional incompressible frictionless flow field is given by $$\large \underset{u}{\rightarrow}=x\hat{i}-y\hat{j}$$ . If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

(A) $$\large \rho \left ( x\hat{i} +y\hat{j}\right )$$

(B) $$\large -\rho \left ( x\hat{i} +y\hat{j}\right )$$

(C) $$\large \rho \left ( x\hat{i} -y\hat{j}\right )$$

(D) $$\large -\rho \left ( x^{2}\hat{i} -y^{2}\hat{j}\right )$$

2. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ______.

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• 3. Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).