Fluid mechanics and mechanical operations 2015

FLUID MECHANICS AND MECHANICAL OPERATIONS QUIZ

Q. 1 Two different liquids are following through different pipes of the same diameter. In the first pipe, the flow is laminar with centerline velocity,V_max,1 ,where as in the second pipe, the flow is turbulent. For turbulent flow, the average velocity is 0.82 time the centerline velocity, V_max,2,For equal volumetric flow rates in both the pipes,te 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 layer, δ at distance x from the leading edge of the plate follows the relation:

δ (x) α x^-1
δ (x) α x
δ (x) α x^1/2
δ (x) α x^-1/2

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: C_D accounts only for the form function
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 a pipe, f doubles on doubling the volumetric flow rate.

R, S, T
P, Q, S
P, R, S
P, Q, S, T

Q. 4 A cylindrical packed bed of height 1m is filled with equal sized spherical particles. The particles are nonporous and have a density of 1500kg/m³. The void fraction of the bed is 0.45. The bed is fluidized using air(density 1kg/m³). If the acceleration due to gravity is 9.8m/s², the pressure drop(in Pa) across the bed at incipient fluidization(up to one decimal place) is.......

Q. 5 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 0.2m diameter. Both the reservoirs are open to atmosphere. The power input to the pump is 90kW 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 1000kg/m³.
The height H, In meters to which the water can be delivered (up to one decimal place) is.......

Q. 6 The diameters of sand particles in a sample range from 50 to 150 microns. The number of particles of diameter x in the sample is proportional to 1/50 + x. The average diameter, in microns (up to one decimal place) is.......

Q. 7 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 viscosities 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.......

Q. 8 A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit operating at constant pressure difference first filters a slurry during which five litres of filtrate is collected in 100s. this is followed by washing, which is done for tw seconds and uses one litre of wash water. assume the following relation to be applicable between the applied pressure drop ΔP, cake thickness L at time t, and volume of liquid V collected in time t:

k₁ and k₂ can be taken to be constant during filtration and washing. The wash time tw, in seconds( up to one decimal place), is.......