BENG1 INTRODUCTION to
THERMO-FLUIDS (THER 103)
TUTORIAL EXAMPLES in APPLICATIONS of BERNOULLI’S EQUATION
Assume: rwater = 103
kg/m3; rmercury = 13.6 x 103 kg/m3;
rair = 1.2 kg/m3
SSL conditions are 101.325 kPa, and 15°C
1.
A pitot-static
tube is used to measure the velocity of an air flow. The static pressure is atmospheric and the
pitot tube, connected to a mercury manometer, shows a difference in levels of
100 mm. Calculate the velocity of the air flow. [149.1 m/s]
2.
A
horizontal Venturi meter has a throat diameter of 50 mm and an inlet to throat
diameter ratio of 2:1. The pressure
difference between the inlet and throat is recorded on a mercury manometer as a
60 mm difference in levels. The
discharge coefficient, Cd, of the meter is 0.95. Calculate the volume flow rate when (i) water
flows through the meter, and (ii) when air flows through the meter.*
3.
Water, drawn from
a reservoir by a pump, is delivered at the rate of 0.1 m3/s to a
point 30 m vertically above the reservoir through a 0.2 m diameter pipe, where
it is discharged to atmosphere. If the total losses in the system amount to 20
times the velocity head in the pipe, determine the power required to drive the
pump which is 66% efficient. What would
contribute to the losses? [59.9 kW]
4.
The pressure at
inlet to a water turbine is recorded on a gauge as 100 kPa at a point where the
pipe is 0.3 m diameter. The flow through the turbine is 0.2 m3/s. The turbine discharges at atmospheric
pressure through a pipe 0.8 m diameter, the exit velocity being lost. The discharge point is 1 m below the inlet. Determine
the output power from the turbine assuming it is 60% efficient. [13.65 kW]
5.
Oil of
relative density 0.85 flows upwards through a vertical Venturi meter fitted in
a 225 mm diameter pipe line. The diameter
of the throat is 75 mm and the throat is 150 mm above the inlet.
Pressure connections are taken from
the inlet and throat of the meter to the lower and upper ends of a vertical
cylinder in which a piston with an area of 1950 mm2 is free to move.
A load can be applied to the piston by
placing masses on a piston rod passing through the cylinder.
Calculate the discharge through the
meter if a load of 13.65 kg, including the piston, is required to maintain the
piston in equilibrium. Neglect frictional
losses.*