Machinery's Handbook, 31st Edition
Flow and Energy Loss in Pipe, Tube, and Fittings 2777 Many other fittings and couplings are available. Couplings attach to the ends of two tubes and have a leak-free means of connecting the halves of the coupling together. Couplings are available with and without shut-off valves to prevent spillage when disconnected. Flow and Energy Loss in Pipe, Tube, and Fittings Fluids experience energy loss due to friction when flowing through pipes and fittings. The energy lost is dependent on the length and diameter of the pipe/tube, the surface con ditions, and the number and shape of any bends or restrictions. Flow Rates.— The principal of continuity for constant flow dictates that the volumetric flow rate (or mass flow rate) remains the same along a pipe, even if the pipe expands, contracts, or is restricted. This means that velocity changes with flow area. One can calculate the velocity before or after a change in flow area if the velocity on the other side of the change is known. Q i A i v i Q o A o v o = = = where A is the cross sectional flow area, Q is volumetric flow rate, and v is velocity. The behavior of a fluid, and its energy losses through pipe and fittings, is dependent upon whether it follows a laminar, transitional, or turbulent flow regime. To determine what flow regime is present, the dimensionless Reynolds number is calculated with the following equations. If the Reynolds number is less than 2000, the flow is laminar. If the Reynolds number is greater than 4000, flow is turbulent. Between those values lies the transitional flow regime. Note that the Reynolds number is dependent on fluid viscosity. R e ρ vD µ = ------ where D is the flow diameter, r is the density, v is the mean velocity, m is the absolute vis cosity of the fluid. R e vD υ ---- QD A υ ----- = = where Q is the volumetric flow rate, A is the cross sectional area of flow, and u is the kine matic viscosity. For general liquid piping applications, the US Army Corps of Engineers manual “Liquid Process Piping” recommends a flow velocity of 7 ± 3 ft/s (2.1 ±0.9 m/s) with a maximum velocity of 7 ft/s at discharge points including pump suction lines and drains. All formulas for calculating the mean velocity of flow through a pipe or tube are approx imate. The following is a formula for low viscosity liquids that will yield results within 5 to 10 percent of actual if applied to carefully laid pipe in fair condition: v C hd = where C is taken from Table 21, h is total head in feet, d is the inside diameter of a round pipe in feet, and L is the total length of the pipe in feet. Length, where pressure drop due to bends and fittings is a factor, is equivalent length. See Energy Loss in Fittings and Valves on page 2783, and Energy Loss in Fittings and Valves on page 2783 for more on this topic. For air, the following velocity equation can be used to estimate flow: v 25 000 dp , L = ------------- p Lv 2 25 000 d , = ------------ where v = velocity of air in feet per second p = loss of pressure due to flow through the pipes in ounces per square inch d = inside diameter of pipe in inches L = length of pipe in feet L 54 d + ----------
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