
1. A twodimensional 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 R_{e}_{D} = 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 ______.

3. Water flows through two different pipes A and B of the same circular crosssection 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 Q_{B}/Q_{A }is ______ (round off to two decimal places).
4. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ________ km/h (The density of air and the frontal area may be assumed to be constant).
5. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ______ kg/s (round off to two decimal places).