Related Resources: calculators

Weymouth Pressure and Flow Formula and Calculator

Fluids Flow Design and Engineering

Weymouth Pressure and Flow Formula and Calculator

Thomas R. Weymouth presented this formula in 1912 for calculating gas flow through high-pressure pipelines. This formula is also used with the flow of compressed air.

Preview Weymouth Pressure Calculator & Weymouth Flow Calculator

The Weymouth friction factor is as follows:

Eq. 1, Imperial units
f = 0.032 / d^0.3333

The Weymouth formula for airflow at standard conditions is

Eq. 2, Imperial units
ΔP = [ ( 1.0457 · 10^-3) · T · L ] / ( P · d^5.3333 ) [ ( P_s · Q_s ) / T_s ]²

Average pressure
Eq. 2a
P = ( P₁ + P₂ ) / 2

also

Eq. 3, Imperial units
Q_s = 21.8742 · T_s / P_s [ ( P₁² - P₂² ) · d^5.3333 ) / ( T · L ) ]^0.5

Where:

ΔP = pressure drop, psi
Q_s = volume flow rate at standard conditions, SCFM
P₁ = upstream pressure, psia
P₂ = downstream pressure, psia
P = average pressure, psia
P_s = pressure at standard conditions, psia
T_s = temperature at standard conditions, °R
d = pipe inside diameter, in
T = airflow temperature, °R
L = pipe length, ft
f = friction factor

Weymouth equation in SI units

Eq. 4
Q = (3.7435 · 10^-3 ) · T_b / P_b · [ P₁² - e^s · P₂² ) / ( G ·t_f · L_e · Z ) )^0.5 · D^2.667 · E

Equivalent length of pipe
Eq. 5
L_e = [ L · ( s^s - 1 ) ] / s

Elevation difference:
Eq. 6
s = 0.0684 ·G · [ ( H₂ - H₁ ) / ( T_f · Z ) ]

Where;

Q = Volume flow rate, standard m³/d
E = Pipeline efficiency, a value less than 1
T_b = base temperature, 'K (273 + 'C)
P_b = base pressure, kPa P1 = upstream pressure, kPa
P₁ = upstream pressure, kPa
P₂ = downstream pressure. kPa
G = gas gravity (air = 1)
T_f = Gas flow temperature at average condition, 'K
L_e = equivalent length of pipe segment, km
L = length of pipe segment, km
Z = gas compressibility factor, dimensionless
D = pipe inside diameter, mm
s = elevation adjustement parameter, dimensionless
H₁ = upstream elevation, m
H₂ = downstream elevation, m

Source:

Piping Calculations Manual 0 2005
E. Shashi Menon, P.E.

Related:

• Babcock Steam Flow Rate Formula and Calculator An empirical equation for steam flow is the Babcock formula.
• Unwin Gas Change of Pressure and Calculator and Formulas The Unwin formula has been successfully used in steam piping calculations for many years.
• Fritzsche Formula for Pressure Change at Standard Conditions Equation and Calculator
• Gas Flow Rate Through Orifice Equations and Calculator per. ISO 5167 ISO 5167 is applicable to orifice plates, nozzles and Venturi tubes when they are inserted in a conduit running full to determine the flow rate of the fluid flowing in the conduit.
• Harris Formula for Pressure Change at Standard Conditions Equation and Calculator
• Swamee-Jain Friction Factor Equation and Calculator This is another explicit equation for calculating the friction factor typically used in the Darcy-Weisbach.
• Venturi Flow Equation and Calculator
• Darcy's Equation Darcy's Equation Fluids Flow Equation - also called Darcy Weisbach equation.
• Flow Losses for Valves and Fittings in Equivalent Feet if Pipe
• Fluid Energy Loss in Fittings and Valves Formula, Calculator and Tables There are two standard ways to calculate the energy lost in fittings and valves: the resistance coefficient method, and the equivalent length method. The method chosen will depend on what information is provided with the fitting to be analyzed.
• Discharge of Air Through An Orifice Discharge of Air Through An Orifice Equation
• Pipe Flow with Gradual Size Enlargement Formula and Calculator
• Pressure Tube Anemometer Air Flow Measurement Equation
• Two-Phase Fluid Flow Two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases
• Water Flow Kinetic Force in Flow Around Submerged Object Calculator and Equation.
• Weir Flow Rectangular Open Channel Water Flow Calculator and Formula