Q 1. Two different liquids are flowing through different pipes of the same diameter. In the first pipe, the flow is laminar with centreline velocity, Vmax,1, whereas in the second pipe, the flow is turbulent. For turbulent flow, the average velocity is 0.82 times the centreline velocity, Vmax,2. For equal volumetric flow rates in both the pipes, the ratio Vmax,1/Vmax,2 (up to two decimal places) is ___________.
Q 2. For uniform laminar flow over a flat plate, the thickness of the boundary layers, δ, at a distance x from the leading edge of the plate follows the relation:
Q 3. For fanning friction factor f (for flow in pipes) and drag coefficient CD (for flow over immersed bodies), which of the following statements are true?
| P: | f accounts only for the skin friction |
| Q: | CD accounts only for the form friction |
| R: | CD accounts for both skin friction and form friction |
| S: | Both f and CD depend on the Reynolds number |
| T: | For laminar flow through pipe, f doubles on doubling the volumetric flow rate |
Q 4. A centrifugal pump delivers water at the rate of 0.22 m3/s from a reservoir at ground level to another reservoir at a height H, through a vertical pipe of 0.2 m diameter. Both the reservoirs are open to the atmosphere. The power input to the pump is 90 kW and it operates with an efficiency of 75%.
Data: Fanning friction factor for pipe flow is f = 0.004. Neglect other head losses. Take gravitational acceleration, g = 9.8 m/s2 and density of water is 1000 kg/m3.
The Height H, in meter, to which the water can be delivered (up to one decimal place) is ________.
Q 5. A spherical solid particle of 1 mm diameter is falling with a downward velocity of 1.7 mm/s through a liquid (viscosity 0.04 Pa.s) at a low Reynolds number (Stokes regime). The liquid is flowing upward at a velocity of 1mm/s. All velocities are with respect to a stationary reference frame. Neglecting the wall effects, the drag force per unit projected area of the particle, in Pa, (up to two decimal places) is _______.
