Problem Sheet – Fluids in Motion
Shane Murray
Dept. of The Built Environment,
Institute of Technology, Carlow
Flow of a frictionless fluid
1. A tank contains oil of relative density 0.85 to a depth of 2.4m. It discharges through a 25mm
diameter straight pipe at a point 6m below the bottom of the tank. Calculate the discharge on
litres per second and tonnes per hour. Find the oil pressure at a point half way along the pipe.
http://screenr.com/wKh & http://screenr.com/8mh & http://screenr.com/Nmh
2. The diameter of a pipe tapers gradually in the direction of the water flow as the level drops
9m from point A to point B. At A the gauge pressure is 210kN/m2 and the pipe diameter is
200mm; at B the diameter is 100mm. What is the pressure at B when the flow rate is 72 litres
per second?
http://screenr.com/dmh & http://screenr.com/Mmh
3. A horizontal pipe taper gradually from 150mm to 300mm diameter in the direction of flow.
At the narrow section a pressure gauge reads 140kN/m2. At the wide section the pressure is
280kN/m2. Neglecting losses, calculate the flow rate of water in cubic metres per second,
litres per second and tonnes per hour.
http://screenr.com/lmh & http://screenr.com/cmh & http://screenr.com/qmh
4. Oil of relative density 0.9 flows through a horizontal pipe which reduces smoothly from
75mm to 50mm diameter. If the gauge pressure at these points is 70kN/m2 and 49kN/m2,
respectively, find the velocity at the larger diameter and the flow rate in tonnes per minute.
http://screenr.com/vmh & http://screenr.com/9mh & http://screenr.com/HRh
5. Oil of relative density 0.8 flows at the rate of 216 litres per second through a falling pipe
which tapers gradually in the direction of flow. The diameter at a point A is 0.6m and at a
point B, 3.6m vertically below A it is 0.3. The gauge pressure as A is 84kN/m2. Calculate the
pressure at B.
http://screenr.com/vOh & http://screenr.com/QOh
Flow of a real fluid
6. A horizontal pipe of 50mm diameter connected to a cylinder of water at 210kN/m2 gauge
pressure discharges freely to the atmosphere. If the head lost to friction in the pipe is 4.2m,
calculate the discharge in litres per minute.
http://screenr.com/POh & http://screenr.com/20h
7. Water is pumped up from a level A to level B, a vertical height of 11m, through a pipe
tapered in diameter from 100mm at A to 150mm at B. The pressure head at A is 24m of water
and at B is 13.5m. The friction loss due to head between A and B is 1.5m. Find the discharge
at B in cubic metres per second and the energy loss due to friction in Watts.
http://screenr.com/90h & http://screenr.com/s4h & http://screenr.com/llh