How to Calculate Pressure Loss
The pressure that a fluid exerts changes as it moves through a pipe. Engineers frequently wish to calculate this pressure when designing systems such as pipelines and plumbing. The calculation of pressure changes is derived from Bernoulli's principle using integral calculus and is based on a variety of factors. However, the calculation can be simplified considerably by making a few assumptions. Does this Spark an idea?
Instructions
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Determine the Reynolds Number from the equation R = dVD/u where R is the Reynold's number, p is the density of the fluid, V is the average fluid velocity, D is the diameter of the pipe and u is the viscosity of the fluid.
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2
Interpret the Reynold's Number as a measure of fluid flow. The Reynold's Number is a dimensionless number that describes the turbulence of a fluid in motion. A Reynold's Number of 2,000 or less indicates a laminar (smooth) fluid flow and a Reynold's Number greater than 4,000 indicates complete turbulence. A Reynold's Number between 2,000 and 4,000 signifies a transitional value between laminar and turbulent flow.
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3
Derive the friction factor. This value will allow us to account for the pressure loss of the fluid due to the friction of the pipe. The friction value f is given by f = 64/R for a laminar fluid flow. We will use this value since the fluid flow in commercial piping is typically laminar.
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Make some simplifying assumptions. For typical calculations of pressure loss, we may assume that the pipe does not have sharp bends and the pipe diameter is constant. This allows us to further assume that the fluid velocity is constant.
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Calculate the pressure differential as Pb = Pa -- dg [h + fLV^2/D2g] = Pa -- dg [h + (64)LV^2/RD2g] where Pa is the pressure at point a and Pb is the pressure at point b. The density of the fluid is d, L is the length of the pipe, V is the fluid velocity, R is the Reynold's Number and D is the diameter of the pipe. Furthermore, h is the height differential between points a and b such that h is positive if b is higher than a. The gravity acceleration constant of 9.8 m/s^2 is represented by g.
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