Leak Rate Calculator (2024)

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Water Leak from Hole in Copper Pipe (photograph)

Leak Rate Equations

Leak Rate
Leaks are common occurrences in pipes, tubes, and tanks. The leak rate is based on the pressure difference between the inside and outside of the pipe, the crack or hole area, and specific gravity of the liquid. The pipe leak rate calculator computes the leak rate of a liquid out of a circular or non-circular crack or hole in a pipe or tank. The leak rate calculation has built-in specific gravity values for water, seawater, diesel fuel, SAE 30 oil, and gasoline. Specific gravity can be entered for other liquids. If the leak rate is known, the calculator can compute pressure or crack area (and diameter).

Leak Rate Equations and Derivation

Liquid inside a pipe, tank, or other confined space flows out through a hole or crack. The liquid in the pipe is at an elevation Z₁, has pressure P₁, and has velocity V₁. As the liquid exits the hole, it increases to velocity V₂ through the hole, pressure P₂ at the hole exit, and an elevation Z₂ of the hole exit.

Diagram of liquid flowing out of pipe through crack:

The Bernoulli equation (Munson et al., 1998, p. 114; bernoulli.php) describes flow of an inviscid fluid flowing from location 1 to location 2.

Solve for V₂:

Then with Q=V₂A₂, A=πd² / 4, and ΔP=P₁-P₂:

Due to the viscosity of liquids and the tortuous path of the liquid through the hole, the measured leak rate from a hole is less that that computed by the above equation. To account for these effects, a discharge coefficient C is commonly used in the equation (e.g. Munson et al., 1998, p. 531; McAllister, 2005, p. 356):

C=0.61 is a typical value determined from experiments (McAllister, 2005, p. 356). Velocity out of the hole is computed approximately as:

A more accurate computation of velocity can be found using the methods at our Discharge from a Tank calculation which splits C into a velocity coefficient and a contraction coefficient. Our Bernoulli equation calculator applies the Bernoulli equation to many situations including pipe leak, but does not include a discharge coefficient.

Variables
The units shown for the variables are SI (International System of Units); however, the equations above are valid for any consistent set of units. Our calculation allows a variety of units; all unit conversions are accomplished internally.
A = Hole or crack area (m²).
C = Discharge coefficient. Need 0 < C ≤ 1. Suggested value is C=0.61 (McAllister, 2005, p. 356). For highly viscous liquids, C is lower.
d = Hole diameter (m).
g = Acceleration due to gravity, 9.8066 m/s².
Q = Leak rate (m³/s).
S = Liquid specific gravity. In calculation, S for water is from Munson et al. (1998, p. B.2); seawater, SAE 30 oil, and gasoline are from Munson Table 1.6; and diesel is from Chevron (2007, p. 48).
V = Leak velocity (m/s).
ΔP = Pressure drop from inside of pipe to outside of pipe (or tank) (N/m²).
ρ_w,std = Mass density of water at standard conditions (4^oC), 1000 kg/m³.
π = 3.1415926...

Error Messages given by calculation
"Need A > 0", "Need 0 < C ≤ 1", "Need d > 0", "Need S > 0", "Need Q > 0","Need ΔP > 0".

Related calculations:

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Bernoulli applications

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Other information:

Unit Conversions Calculator

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