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Material and energy

Fluid-flow theory
Fluid-flow applications
Heat-transfer theory

separation processes


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1. The static pressure in a fluid, at a depth Z, is given by:

                           P =Zrg
taking the pressure at the fluid surface as datum.

2. Fluid flow problems can often be solved by application of mass and energy balances.

3. The continuity equation, which expresses the mass balance for flow of incompressible fluids, is:

                      A1v1 = A2v2.

4. The Bernouilli equation expresses the energy balance for fluid flow:

gZ1 + v12/2 + P1/r1 = gZ2 + v22/2 + P2/r2

Friction and other energy terms can be inserted where necessary.

5. The dimensionless Reynolds number (Re) characterizes fluid flow, where

                       (Re) = (Dvr/m)

For (Re) < 2100, flow is streamline, for (Re) > 4000 flow is turbulent, and between 2100 and 4000 the flow is transitional.

6. Friction energy loss in pipes is expressed by the equation:

Eƒ = (4ƒv2/2) x (L/D)

and pressure drop in pipes:

DP = (4ƒrv2/2) x (L/D).


1. In an evaporator, the internal pressure is read by means of a U-tube containing a liquid hydrocarbon of specific gravity 0.74. If on such a manometer the pressure is found to be below atmospheric by 83 cm, calculate (a) the vacuum in the evaporator and estimate (b) the boiling temperature of water in the evaporator by using the steam tables in Appendix 8.
[(a) 6.025 kPa ,absolute pressure 95 kPa; (b) 98.1 °C]

2. Estimate the power required to pump milk at 20°C at 2.7 m s-1 through a 4 cm diameter steel tube that is 130 m long, including the kinetic energy and the friction energy.
[ 297.05 J s-1 = 0.4 HP]

3. A 22% sodium chloride solution is to be pumped up from a feed tank into a header tank at the top of a building. If the feed tank is 40 m lower than the header and the pipe is 1.5 cm in diameter, find (a) the velocity head of the solution flowing in the pipe, and (b) the power required to pump the solution at a rate of 8.1 cubic metres per hour. Assume that the solution is at 10°C, pipeline losses can be ignored, the pump is 68% efficient, and that the density of the sodium chloride solution is 1160 kg m-3.
[(a) 8.2 m , (b) 2.42 HP]

4. It is desired to design a cooler in which the tubes are 4 cm diameter, to cool 10,000 kg of milk per hour from 20°C to 3°C. Calculate how many tubes would be needed in parallel to give a Reynolds number of 4000.
[ 11 tubes ]

5. Soyabean oil is to be pumped from a storage tank to a processing vessel. The distance is 148 m and included in the pipeline are six right-angle bends, two gate valves and one globe valve. If the processing vessel is 3 m lower than the storage tank, estimate the power required to pump the oil at 20°C, at the rate of 20 tonnes per hour through the 5 cm diameter pipe assuming the pump is 70% efficient.
[ 41 HP ]

6. In the design of an air dryer to operate at 80°C, the fan is required to deliver 100 cubic metres per minute in a ring duct of constant rectangular cross-section 0.6 m by 1.4 m. The fan characteristic is such that this delivery will be achieved so long as the pressure drop round the circuit is not greater than 2 cm of water. Determine whether the fan will be suitable if the circuit consists essentially of four right-angle bends of long radius, a pressure drop equivalent to four velocity heads in the bed of material and one equivalent to 1.2 velocity heads in the coil heater. Assume density of water os 1000 kg m-3.
[ Z water = 0.124 cm, < 2 cm water ]


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Unit Operations in Food Processing. Copyright © 1983, R. L. Earle. :: Published by NZIFST (Inc.)
NZIFST - The New Zealand Institute of Food Science & Technology