###### Introduction to Fluid Mechanics and Fluid Machines

206 SOLVED PROBLEMS

Question: 12.1

## The depth of a uniform steady flow of water in a 1.22 m wide rectangular cement lined channel laid on a slope of 4 m in 10000 m, is 610 mm. Find the rate of discharge using Manning’s value for c (Chezy coefficient). ...

We have to use Eq. (12.9) for the present purpose....
Question: 6.11

## The capillary rise h, of a fluid of density ρ, and surface tension σ, in a tube of diameter D, depends upon the contact angle φ, and acceleration due to gravity g. Find an expression for h in terms of dimensionless variables by Rayleigh’s indicial method. ...

Capillary rise $h$, is the dependen...
Question: 6.9

## In the study of vortex shedding phenomenon due to the presence of a bluff body in a flow through a closed duct, the following parameters are found to be important: velocity of flow V, density of liquid ρ, coefficient of dynamic viscosity of liquid μ, hydraulic diameter of the duct Dh, the width ...

The problem is described by 6 variables  V,...
Question: 8.2

## Two viscous, incompressible, immiscible fluids of same density (=ρ) but different viscosities (viscosity of the lower fluid layer = μ1 and that of the upper fluid layer = μ2 < μ1) flow in separate layers between parallel boundaries located at y = ± H, as shown in the Fig. 8.6. Thickness of each ...

Large lateral width of the plate renders the basic...
Question: 5.15

## A lawn sprinkler discharges water upward and outward from the horizontal plane, as shown in Fig. 5.20. Initially, the angular speed of the sprinkler is zero. The total volumetric rate of discharges through the sprinkler is Q. If the area of cross section of the sprinkler arms and the discharging ...

Approach 1: Moving Reference Frame Angular momentu...
Question: 16.8

## A centrifugal fan running at 1500 rpm has inner and outer diameter of the impeller as 0.2 m and 0.24 m. The absolute and relative velocities of air at entry are 21 m/s and 20 m/s respectively and those at exit are 25 m/s and 18 m/s respectively. The flow rate is 0.6 kg/s and the motor efficiency ...

(i)      U_{1}=\frac{\pi \times 0.20 \times...
Question: 16.7

## The preliminary design of an axial flow compressor is to be based upon a simplified consideration of the mean diameter conditions. Suppose that the characteristics of a repeating stage of such a design are as follows: Stagnation temperature rise (ΔTst) 30 K Degree of reaction (Λ) 0.6 Flow ...

Specific work input        w=1005 \times 30...
Question: 16.6

## The conditions of air at the entry of an axial flow compressor stage are p1 = 100kN/m^2 and Tl = 300 K. The air angles are β1 = 51º, β2 = 10º, a1 = a 3 = 8º. The mean diameter and peripheral speed are 0.5 m and 150 m/s respectively. Mass flow rate through the stage is 30 kg/s; the work done ...

(i)  \rho_{1}=\frac{p_{1}}{R T_{1}}=\frac{1...
Question: 16.5

## At the mean diameter, U = 200 m/s, V f = 180 m/s, β1 = 43.9° and β2 = 13.5°. The factor λ = 0.86 and ηs = 0.85 and inlet temperature T1t is 288 K. Calculate the pressure ratio. ...

 \Delta T_{s t}=\frac{0.86 \times 200 \time...
Velocity of the blade tip,  U_{2}=\frac{\pi...