Pressure Drop in Pipes
Pressure drop is decrease in pressure from one point in a pipe or tube to another point downstream. Pressure drop occurs due to frictional forces acting on a fluid as it flows through the tube. The frictional forces are caused by the resistance to flow. The main determinants of resistance to fluid flow are fluid velocity through the pipe and fluid viscosity. Any liquid or gas will always flow in the direction of least resistance (less pressure). Pressure drop increases proportional to the frictional shear forces within the piping network. A piping network containing a high relative roughness rating as well as many pipe fittings and joints, tube convergence, divergence, turns, surface roughness and other physical properties will affect the pressure drop. High flow velocities and / or high fluid viscosities result in a larger pressure drop across a section of pipe or a valve or elbow. Low velocity will result in lower or no pressure drop. Pressure Drop can be calculated using two values: the Reynolds Number, Re (determining laminar or turbulent flow), and the relative roughness of the piping. The velocity of hydraulic fluid through a conductor (pipe, tube or hose) is dependent on flow rate and cross sectional area. Recommended fluid velocities through pipes and hoses in hydraulic systems are as follows:
Alternatively, fluid velocity can be calculated using the following formula: Q × 0.408 v = -------------- D ^{2}Where: v = velocity in feet per second (ft/sec) Q = flow rate in US gallons per minute (US gpm) D = inside diameter of pipe or hose in inches (in).
If the Reynolds Number is between 2300 and 4000, flow is transition and greater than 4000 flow is turbulent. For Reynolds Numbers greater than 2300 and less than 100,000 the following formula can be used to calculate the friction factor:
H = K (v ^{2}/2g)where, H = Head loss, m V = Velocity of flow, m/s Pressure drop or head loss, occurs in all piping systems because of elevation changes, turbulence caused by abrupt changes in direction, and friction within the pipe and fittings. The most common methods used to determine the head loss in fiberglass pipe are Hazen-Williams, Manning and Darcy-Weisbach equations. The suitability of each method depends on the type of flow (gravity or pumped) and the level of accuracy required. Due to the smooth inside surface and the resistance to corrosion, ADPF fiber glass pipes have a relatively low head loss as compared to other material pipes. Hazen-Williams Equation: The Hazen-Williams Equation is applicable to water pipes under conditions of full turbulent flow. It has gained wide acceptance in the water and wastewater industries because of its simplicity.v = 0.85 C R ^{0.63}J^{0.54}where, v = velocity, m/s C = Hazen-Williams Coefficient R = Hydraulic mean radius, m J = Hydraulic gradient, m/m Hazen-William coefficient, C for ADPF fiber glass pipe is taken as 150. Manning Equation: The Manning equation typically solves gravity flow problems where the pipe is only partially full and is under the influence of an elevation head only.v = (1/n) R ^{0.667} J^{0.5}
where,v = velocity, m/s n = Manning Coefficient R = Hydraulic mean radius, m J = Hydraulic gradient, m/m Manning Coefficient, n for ADPF fiber glass pipe is taken as 0.01 Darcy-Weisbach Equation: It states that pressure drop is proportional to the square of the velocity and the length of the pipe. This equation is valid for all fluids in both laminar and turbulent flow. The disadvantage is that the Darcy-
Weisbach friction factor is a variable.
J = ( f.L.v^{2})/2.g.D
where,J = Head loss, m g = Gravity constant, 9.81 m/s ^{2}v = Velocity, m/s D = Inside diameter, m f = Friction factor L = Length of the pipe, m The well known Reynolds number equation is used to characterize the fluid flow. If the flow is Laminar, f = 64 / Re If the flow is Turbulent, the friction factor can be determined from the Moody diagram found in most fluid mechanics texts or calculated from the Colebrook equation. Pressure drop in fittings: Head Loss in Fittings is frequently expressed as the equivalent length of pipe that is added to the straight run of pipe as shown below. This approach is used most often with the Hazen-Williams or
Manning equations. The approach does not consider turbulence and subsequent losses created by different velocities.
Surge pressure (Water Hammer): Pressure surge or Internal shock, known commonly as water hammer, results from abrupt change of velocity within the system. Under certain conditions, these shock forces can reach magnitude sufficient to rupture or collapse a piping system, regardless of the material of construction. The transient pressure is the rapidly moving wave which increases and decreases the pressure in the system depending on the source of the transient and direction of wave travel. Rapid valve closure can result in the build-up of shock waves due to the conversion of kinetic energy of the moving fluid to potential energy which must be accommodated. These pressure waves will travel throughout the piping system and can cause damage far away from the wave source. The magnitude of the water hammer depends on- Fluid properties
- Velocity of flow
- Modulus of Elasticity of the pipe material
- Length of the pipe line
- Speed in which the momentum of the fluid changes
where, a = Wave velocity (ft/s) P = Surge Pressure (psi) v = Change in flow velocity (ft/s) w = Density of fluid (lb/ft ^{3})SG = Specific gravity of fluid K = Bulk modulus of fluid (psi) E = Hoop modulus of elasticity (psi) d = Inside diameter of pipe (inch) t = Pipe wall thickness (inch) g = Acceleration due to gravity (ft/s ^{2})Good design practice usually prevents water hammer in most systems. Installation of valves which cannot open or close rapidly is one simple precaution. In addition, pumps should never be started into empty discharge lines unless slow opening mechanically actuated valves can increase the flow rate gradually. Check valves on pumps should close as quickly as possible to minimize the velocity of fluid flowing back. In some cases, thoroughly anchoring the piping system may mitigate this problem. In other cases, mechanical valve operators, accumulators, or feedback loops around pumps may have to be used to remove the source of water hammer. |