1. The static pressure in a fluid, at a depth Z, is given by:
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:
4. The Bernouilli equation expresses the energy balance for fluid flow:
Friction and other energy terms can be inserted where necessary.
5. The dimensionless Reynolds number (Re) characterizes fluid flow, where
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:
and pressure drop in pipes:
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
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.
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.
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
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.
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 ]
CHAPTER 4: FLUID-FLOW APPLICATIONS
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