Physical properties of fluid and fluid transport in piping system

Laminar and turbulent flow in pipe

Fluid flow equation

Flow in pipes and valves theory - full content

As in real piping system, losses of energy are existing and energy is being added to or taken from the fluid (using pumps and turbines) these must be included in the Bernoulli equation.

For two points of one streamline in a fluid flow, equation may be written as follows:

where is:

• Z_1,2 - elevation above reference level
• p_1,2 - absolute pressure
• v_1,2 - velocity
• &rho_1,2 - density
• h_L - head loss due to friction in the pipe
• H_p - pump head
• H_T - turbine head
• g - acceleration of gravity

From Bernoulli equation all other practical formulas are derived, with modifications due to energy losses and gains.

Flow in pipe is always creating energy loss due to friction. Energy loss can be measured like static pressure drop in the direction of fluid flow with two gauges. General equation for pressure drop, known as Darcy's formula expressed in meters of fluid is:

where is:

• h_L - head loss due to friction in the pipe
• f - friction coefficient
• L - pipe length
• v - velocity
• D - internal pipe diameter
• g - acceleration of gravity

To express this equation like pressure drop in newtons per square meter (Pascals) substitution of proper units leads to:

where is:

• &Delta p - pressure drop due to friction in the pipe
• &rho - density
• f - friction coefficient
• L - pipe length
• v - velocity
• D - internal pipe diameter
• Q - volumetric flow rate

The Darcy equation can be used for both laminar and turbulent flow regime and for any liquid in a pipe. With some restrictions, Darcy equation can be used for gases and vapors. Darcy formula applies when pipe diameter and fluid density is constant and the pipe is relatively straight.

<< Measurement of pressure -- Friction factor >>