# How to calculate equivalent flow resistance K for pipes

Knowing the equivalent flow resistance, identified by the letter K in equations, is necessary to determine the pressure within a network of pipes.

## Calculation for Pipes in Series

The resistance value for pipes mimics the resistance found in electrical circuits.
The steps for determining the equivalent flow resistance K differs on whether the pipes are in series or in parallel.

Find the length and diameter of each pipe section using calipers or measuring tape. For example, pipe 1 is two meters long and one meter in diameter, while pipe 2 is three meters long and one meter in diameter.

Look up the friction factor for each section of pipe; this is often provided by the pipe manufacturer. If the friction factor is not known, it can be calculated from the Reynolds number. Reynold's numbers range from 1 to 2000 for laminar flow and from 2000 to 200,000 for highly turbulent flow. For laminar, non-turbulent flow, the friction factor can be found by dividing 64 by the Reynolds number for the type of fluid flow. In this example, assume a very smooth flow with little resistance from the pipe or turbulence, giving a Reynolds number of 64. Dividing the number 64 by the Reynolds number 64 gives a friction factor of 1.00.

Find the resistance K for each of the section of pipe. K for each section of pipe equals the friction factor multiplied by the length, divided by the diameter. The length and diameter need to be the same units so that the resulting K is dimensionless. Pipe 1 is 2 meters long and 1 meter in diameter. For a pipe that is 2 meters long, 1 meter in diameter, and has a friction factor of 1.0, the equation to find K is 1 x 2.0 /1 = 2.0. In this case, the K value for pipe 1 equals 2.0. Pipe 2 is 3 meters long and 1 meter in diameter. For a pipe that is 3 meters long, 1 meter in diameter, and has a friction factor of 1.0, 1 x 3.0 /1 = 3.0. In this case, the K value for pipe 2 equals 3.0.

Calculate the equivalent flow resistance K by finding the sum of all sections of pipe. If one pipe has a K value of 2 and a second pipe has a K value of 3, then 2 + 3 = 5. The equivalent flow resistance, Keq, is 5.

## Calculation for Pipes in Parallel

Find the length and diameter of each pipe section using calipers or measuring tape. For example, pipe 1 is two meters long and one meter in diameter, while pipe 2 is three meters long and one meter in diameter.

Look up the friction factor for each section of pipe; this is often provided by the pipe manufacturer. If the friction factor is not known, it can be calculated from the Reynolds number. Reynolds numbers range from 1 to 2000 for laminar flow and from 2000 to 200,000 for highly turbulent flow. For laminar, non-turbulent flow, the friction factor can be found by dividing 64 by the Reynolds number for the type of fluid flow. In this example, we will assume a very smooth flow with little resistance from the pipe or turbulence, giving a Reynolds number of 64. Dividing the number 64 by the Reynolds number 64 gives a friction factor of 1.00.

Find the resistance K for each of the section of pipe. K for each section of pipe equals the friction factor multiplied by the length, divided by the diameter. Pipe 1 is 2 meters long and 1 meter in diameter. For a pipe that is 2 meters long, 1 meter in diameter, and has a friction factor of 1.0, the equation to find K is 1 x 2.0 /1 = 2.0. In this case, the K value for pipe 1 equals 2.0. Pipe 2 is 3 meters long and 1 meter in diameter. For a pipe that is 3 meters long, 1 meter in diameter, and has a friction factor of 1.0, 1 x 3.0 /1 = 3.0. In this case, the K value for pipe 2 equals 3.0.

Calculate the equivalent parallel flow resistance using the relationship 1/sqrt(Keq) = 1/sqrt(K1) + 1/sqrt(K2). If one pipe has K value of 2 and a second pipe has a K value of 3, this equation would be 1/(sqrt2) + 1/(sqrt2). The square root of 2 is 1.414, and the inverse of this value is 0.7071. The square root of 3 is 1.732, and the inverse of this value is 0.5774. Adding the inverses of the square roots gives 0.5774 + 0.7071 = 1.2845; this is the inverse square root of Keq, not the total.

Find Keq by finding the inverse and then squaring it. Find the inverse of 1.2845 and then square it. The inverse of 1.2845 is 0.7785, and the square of 0.7785 is 0.60608.

## Things You Will Need

• calipers or measuring tape

## Tip

• Resistance is lower in parallel pipe flow because there are multiple paths the flow can take.

## Warning

• The length and diameter need to be the same units so that the resulting K is dimensionless. So if one of the dimensions is in feet and the other dimension is in inches, convert the measurement in inches to feet before finding K.