FLUID MECHANICS

Oct/Nov.2004

Time:3hours

THE KENYA NATIONAL EXAMINATIONS COUNCIL

HIGHER DIPLOMA IN MECHANICAL ENGINEERING

INSTRUCTIONS TO CANDIDATES:

You should have the following for this examination:

Answer book.

Drawing instruments.

Mathematical tables/Scientific calculator.

Answer any FIVE of the following EIGHT questions.

All questions carry equal marks.

Maximum marks for each part of the question are shown.

1.(a) Working from first principles obtain the Poiseuille equation.

Q=p(P1-P2)R48µL

Where Q=flow rate.

P1-P2=Pressure difference.

R=radius of the pipe.

?=dynamic viscosity of the fluid.(11marks)

(b) A pump at one end of a pipeline is required to pump 50×103 Kg/hr of oil along,100mm diameter pipeline,into a receiver at atmospheric pressure.The oil has a density of 850 Kg/m3 and a kinematic viscosity of 0.0188m2/s.Show that the flow is laminar and calculate the power required to drive the pump assuming an efficiency of 0.75(9marks)

2.(a) With the aid of a sketch,explain the working principle of an impulse water turbine.(4marks)

(b) The mean blade circle diameter of the runner of an axial-flow impulse turbine is 1350mm.The guide blade angle is 240,the receiving and discharging angles of the runner being 480 and 230,respectively.The breath of the moving blades at inlet is 100mm.The turbine is working under a head of 85m. Determine;

(i) the speed of the turbine so that the water may pass smoothly on the blades.

(ii) The power developed by the turbine if at full circumferential admission the passages are 85% full at inlet.(16marks)

3.The operating characteristics of a centrifugal pump running at a constant speed of 1200rev/min are given in table 1 below:

Head,H(m)—-27.8—–26.5—-23.6—-19.8-14.7 Discharge Q(m3/min)—0.6-1.2-1.8—2.4-3.3 Efficiency n(%)—75-79-81—79—-75 TABLE 1

The pump is to be coupled to an electric motor running at 1450rev/min and to discharge into a pipe for which the head loss is given by

h=3.6Q2

Where Q=volumetric flow rate,m3/min.

h=head in meters.

The discharge point from the pipe is 20m above the pump.

Plot the operating characteristics and hence determine the discharge of the pump and power required to operate it.

4.(a) Using Buckingham p method show that the flowrate Q(m3/s) through an orifice at the bottom of a tank is given by

Q=vp/?D2 Ø[(D/H)(µ/vgH?D)(d/?gH2)]

In which P is the pressure on the water,?mass density,µviscosity,D diameter of orifice height of orifice from ground,d surface tension and Ø means “a function of”.(14marks)

(b) The loss of head in a pipe 25mm in diameter and 35m long,through which water is flowing at 3m/s,was found to be 25m of water.Calculate the loss of head in a 75mm diameter pipe and 20m long in which air is flowing.For air,?=1.3Kg/m3,µ=1.8×10-5NS.m2.For water,?=103 Kg/m3,µ=1.2×10-3Ns/m2.(6marks)

5.(a) Determine an expression for the critical depth in a trapezoidal channel.(8marks)

(b)In a venture flume the bed is horizontal and the throat is rectangular.The width of the throat is 0.3m and the width of inlet is 0,45m.

On the downstream side a “jump” occurs so that the conditions for maximum flow exist at the throat.If the rate of flow is 0.05m3/sec and coefficient of discharge to be unity,calculate the:

(i) depth of water at the throat.

(ii) depth of water at inlet.(12marks)

6.(a) Explain what is meant by the specific speed of a centrifugal pump and show that the value is given by:

Ns=NvQ/H¾

Where N is the rotational speed of the impeller,Q the discharge and H the operating head.(13marks)

(b) A pump operating at 1500rev/min at maximum efficiency discharges 12.5m3/min under a head of 26.5.Calculate the:

(i) specific speed for this pump.

(ii) discharge and head to be expected from geometrically similar pump twice as big running at the same speed.(7marks)

7.(a) Show from first principles that for maximum flow conditions of a compressible gas through a nozzle,the velocity is given by:

V2=vrp2/v?2

Where p2=pressure immediately in front of nozzle.

?2 =density of the gas

r=the adiabatic expansion index. (12marks)

Assume adiabatic conditions.

(b) A nozzle having a throat diameter 25mm is fitted in the side of a tank containing air at a pressure of 8bar and atmospheric temperature of 15OC.Calculate the:

(i) velocity of the gas in the nozzle.

(ii) back pressure for maximum discharge through the nozzle.

(iii) volumetric flow rate in the nozzle.(8marks)

8.(a) Obtain a formula for the rise in pressure in a thin elastic pipe of a circular section in which flow of water is stopped by the sudden closing of a valve assuming the following symbols to be used:

?=water density

E=modulus of elasticity of pipe material

K=bulk modulus of elasticity for water

V=Poisson’s ratio

t=thickness of pipe

V=velocity of flow

d=diameter of pipe

d?=change of pressure(15marks)

(b) Water supply to a system flows along a pipe which is 150mm in diameter and 6.25mm thick with a velocity of 1.4m/s,when it is suddenly brought to rest by closing a valve.Calculate the theoretical stress produced in the pipe near the valve taking K=2.07x109N/m2,?=103 kg/m3for water;and v=0.25 and E=124×109 N/m2 for pipe material.(5marks)