Department of Machanical Engineering

27/11/2017

BAŞKENT UNIVERSITY

DEPARTMENT OF MACHANICAL ENGINEERING

MAK-307 FLUID MECHANICS-I

HOMEWORK-II

SOLUTION

Q.1. Air, as a working fluid, steadily flows through the fluid machine as shown in figure. Determine;

a) Exit velocity ,

b) Head power transferred.

Ç.6.

a)Akışkan hava olduğuna göre Hal dneklemi kullanılarak çıkış ve giriş kesidinde yoğunluk,

r=P/(RT)

Denkleminden,

r1=1034000/(287x422)=8.5kg/m3

r2=275000/(287x275)=3.45kg/m3

Giriş debisi;

m1=r1A1V1=8.5xp/4x0.152=4.6kg/s

Kütlesel debi bilindiğine göre çıkış hızı;

m1=m2=r2A2V2….. V2=74 m/s

b) Enerji korunmu denklemi uygulanarak,

Q-W=m2(CPT2+(1/2)V22 )-m1(CPT1+(1/2)V21)

W=522000 Watt ( Çevreye karşı iş yapıldığından pozitiftir)

CP=1003Nm/kgK

Sayısal değerler denkleme taşınarak,

Q=-664 kW

Q.2. Milk with a density of 1020 kg/m3 is transported on a level road in a 9-m-long, 3-m-diameter cylindrical tanker. The tanker is completely filled with milk (no air space), and it accelerates at 4 m/s2. If the minimum pressure in the tanker is 100 kPa, determine the maximum pressure difference and the location of the maximum pressure.

Sol.

Pressure distribution in the tank;

Minimum pressure obtained at the point A,

Maximum pressure can be obtained at the point B.

Maximum pressure difference is;

PB –PA=204040-100000=104040 Pa

Q.3. A 1.2-m-diameter, 3-m-high sealed vertical cylinder is completely filled with gasoline whose density is 740 kg/m3. The tank is now rotated about its vertical axis at a rate of 70 rpm. Determine (a) the difference between the pressures at the centers of the bottom and top surfaces and (b) the difference between the pressures at the center and the edge of the bottom surface.

PA=hAxrg=(3-0.96)x740x10=15096Pa

PO=0

PC=hC(rg)=3x740x10=22200Pa

PC-PA=22200-15096=7104Pa

Q4. A sealed box filled with a liquid shown in the figure can be used to measure the acceleration of vehicles by measuring the pressure at top point A at back of the box while point B is kept at atmospheric pressure. Obtain a relation between the pressure PA and the acceleration a.

Sol.

Pressure distribution;

C=?

Pressure equation is,

Applying Eq. To the point A,

Q5. A steady, two-dimensional velocity field is given by

Calculate constant c such that the flow field is irrotational.

Sol.

For irrotational flow field the vorticity has to be zero,

Q6. An oil pump is drawing 25 kW of electric power while pumping oil with density 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm,

respectively. If the pressure rise of oil in the pump is measured to be 250 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump. Take the kinetic energy correction factor to be 1.05.

Sol. Applying energy equation,

Motor power,

Q7. Calculate the power of the pump of the system given below. Note: Total energy loss of the system is 2 meter water column and the specific of the fluid is 1.025, the efficiency of the pomp is 75%..

Sol.

Applying Bernoulli equation between Points (1) and (2)

As points (1) and (2) ar open to atmosphere,

Using conservation of mass,

V1A1=V2A2®V1=4.2 m/s

Pump power,

W= gQhP=10000x(V1A1)x72.42=10000x0.074x72.42=53750.2Watt=53.7502kW

Consideringthe efficiency of the pump, power needed,

W=53.7502/h=53,7502/0,75=71.666kW

S.8. Determine torque acting on the connection A. Note: System is in the vertical plane. Fluid is water, r=1000 kg/m3.

sol.

Applying the angular momentum equation,

As flow is steady,

P2 is obtained from the Bernoulli equation, applying between points (1) and (2),

Putting all the values in the angular momentum equation, torque can be calculated.