SCHOOL of ENGINEERING               UNIVERSITY of PLYMOUTH                                   

 

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.*