# Pipe Flow Calculation: GPM Through Pipe Level Section

• George Steel
In summary, the conversation discussed a unique and simple method for determining the flow volume through a pipe using a slide chart. The method involves measuring the horizontal distance of the flow stream after it drops 4 inches and using this value to solve an equation based on the pipe size. The equation takes into account the acceleration due to gravity and the initial velocity of the flow stream. The conversation also touched upon the physics of trajectories and provided the basic equation for calculating the vertical location of a projectile. The conversation concluded with a clarification of the correct value for the acceleration due to gravity in the equation.
George Steel
I used to have a slide chart that gave gpm through a level section of pipe (1/2" - 6") by measuring how long the exit stream was when it had dropped 4". Imagine a framing square with the blade on the pipe and the tongue hanging down in the stream. Slide the square out until the stream is hitting the 4" mark on the tongue - read length from end of pipe on the blade of the square. The slide chart would give the gpm based on various pipe sizes. Has anyone seen one of these charts? Mine was from 30 years ago. Maybe by a water pump company? Can anyone give the equation behind this method?

Thanks

I have not seen this type of instrument but it is a unique and simple solution based upon the following:

The flow volume through a pipe Q = v (pipe flow velocity) x A ( pipe I.D. area), and by having selected the pipe size on the slide chart therefore inside diameter of the pipe it is then only necessary to determine the fluid flow velocity to determine the flow capacity.

Note: For convenience, this analysis will be done in the units of inches and seconds that can then easily be converted to gpm (gallons per min).

The time for the flow stream to drop the specified 4" is t = sqrt(2 x h / g), where g (the acceleration due to gravity) = 2.68 inches/second^2, and h = 4 inches:
therefore, t = sqrt(2 x 4 / 2.68) = 1.728 sec;

v (velocity of the stream through the pipe) = s (the horizontal distance from the end of the pipe) / t .

Now, all that is required is the measured horizontal stream distance s to solve the equation: Q (inches^3/sec) = s (in.) / 1.728 (sec) x A (in^2);

and, after units and in^3/gal conversion: Q (gpm) =.15 x s (in.) x A (in^2)

However, the A (area) used in the chart for a given pipe size may also contain an adjustment for flow friction; and, only a comparison of the formula result to the chart result will determine if that is true.

The principle is based on the physics of trajectories, for which the basic equation is:
$$y = -\frac{g\sec^2\theta}{2v_0^2}+x\tan\theta$$
Where:
##y## is the vertical location (m);
##x## is the horizontal location (m);
##\theta## is the angle of elevation;
##v_0## is the initial velocity (m/s);
##g## is the acceleration due to gravity (9.81 m/s²).

In your case, ##\theta## = 0 (so ##\sec^2##0 = 1 and ##\tan##0 = 0), ##y## = -4 in (=-0.1016 m; note the negative sign).

Isolating ##v_0##:
$$v_0 = \sqrt{\frac{-g}{2y}}x = \sqrt{\frac{-9.81}{2 (-0.1016)}}x$$
$$v_0 = 6.95x$$
To get the volumetric pipe flow (m³/s), you multiply the initial flow velocity by the pipe area (##A =\frac{\pi}{4}d^2##; m²):
$$VF = v_0A = 6.95x\frac{\pi}{4}d^2 = 5.457d^2x$$
Using gpm for ##VF## and inches for ##d## and ##x##, you get:
$$VF = 1.4174d^2x$$
So, for example, if it takes 6" for the flow to drop 4", the volumetric flow for a 1" pipe is:
$$VF = 1.4174(1)^2(6) = 8.5 gpm$$

I'm slow to type, so @JBA already answered, but my answer doesn't match his. I've been looking for the error and the problem is the 2.68 in his first equation. It should be 386.1, which is the correct acceleration due to gravity in in/s².

Last edited:
jack action, thank you. As soon as I saw your comment I realized I had divided when I should have multiplied. All of that work totally wasted by a stupid conversion error.

I have now rerun the calculation using the correct value for g = 386.16 in/sec^2 (based upon 32.18 ft/sec^2) and my answer is now equal to yours at VF = 1.4173 x (1)^2 x (6) = 8.504 gpm.

Thanks to you both.. Excellent description.

## 1. How do you calculate the GPM (gallons per minute) through a pipe level section?

The GPM through a pipe level section can be calculated using the following formula: GPM = (π * d^2 * v) / 4, where d is the diameter of the pipe and v is the velocity of the water. This formula is based on the assumption that the pipe is full and flowing at its maximum capacity.

## 2. What is the equation for determining the velocity of water in a pipe?

The velocity of water in a pipe can be calculated using the Bernoulli's equation, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline. In simpler terms, this means that the velocity of water can be calculated by dividing the flow rate (in cubic feet per second) by the cross-sectional area of the pipe.

## 3. How does the pipe diameter affect the GPM flow rate?

The pipe diameter has a direct impact on the GPM flow rate. The larger the diameter of the pipe, the higher the flow rate will be. This is because a larger pipe has a larger cross-sectional area, allowing more water to pass through at a given velocity. Conversely, a smaller pipe diameter will restrict the flow rate and result in a lower GPM.

## 4. What other factors besides pipe diameter can affect the GPM flow rate?

Besides pipe diameter, other factors that can affect the GPM flow rate include the viscosity of the fluid, the length and roughness of the pipe, and the pressure drop across the pipe. These factors can impact the flow rate by changing the velocity of the water as it travels through the pipe.

## 5. How do you account for pressure changes along the pipe when calculating the GPM flow rate?

To account for pressure changes along the pipe, the Darcy-Weisbach equation can be used. This equation takes into consideration the frictional losses caused by changes in pressure, flow rate, and pipe properties. It is more complex than the basic GPM formula but provides a more accurate calculation for flow rate in real-world scenarios.

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