Pipe Leak Rate due to Pressure Drop using EMT

Topic: Pipe Leak Rate due to Pressure Drop;

Subject: Fluid Mechanics or Hydraulics;

Tool: Euler Math Toolbox (EMT);

by: Gani Comia, Nov. 2024;

This handy calculation toolbox was created to estimate the water leak rate due to pressure drop in a firefighting system of a building. The situation here was that the fire pump automatically shuts off after reaching the 100 psi high pressure setting. It was observed that the pressure was dropping down with all the gate valves closed. The pressure reached 20 psi in just 18 minutes. 

Below is an estimation of the water leak rate using EMT.

EMT Script.

Pipe Leak Rate due to Pressure Drop

The leak rate calculation for incompressible fluid due to pressure drop is:

Q=ΔpVt$$\frac{\mathrm{<br>}}{}$$

Given:

>p1 = 100*6.9;                // kPa (100 psi), initial pressure
>p2 = 20*6.9;                 // kPa ( 20 psi), final pressure
>t  = 18;                     // min, time duration of pressure drop

Pipe network data.
Pipe size : Dia 38mm GI Pipe S40
Pipe length : 342 m

>pipeId = (38-2*1.5)/1000;       // m, inside dia, GI pipe S40 38mm
>areaId = (1/4)*%pi*(pipeId)^2;  // m^2, area, GI pipe S40 38mm
>pipeLg = 342;                   // m, total pipe length
>V  = areaId*pipeLg;             // m3,  volume of system under test

Leak rate calculation.

>function Q(p1,p2,V,t) := ((p1-p2)*V)/t

Leak rate, [L/min].
Note: 1 kPa m^3 ~ 1 Liter

>leakRate = Q(p1,p2,V,t);
>"Leak rate: " + leakRate + " L/min for 1 kPa pressure drop."

Leak rate: 10.0906385237 L/min for 1 kPa pressure drop.

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