# Fluid Mechanics GATE-2015

**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, V_{max,1}, whereas in the second pipe, the flow is turbulent. For turbulent flow, the average velocity is 0.82 times the centreline velocity, V_{max,2}. For equal volumetric flow rates in both the pipes, the ratio V_{max,1}/V_{max,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 C_{D} (for flow over immersed bodies), which of the following statements are true?

P: | f accounts only for the skin friction |

Q: | C_{D} accounts only for the form friction |

R: | C_{D} accounts for both skin friction and form friction |

S: | Both f and C_{D} 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 m^{3}/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/s^{2} and density of water is 1000 kg/m^{3}.

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 _______.