The flow rate of a gas describes the volume of gas that passes a particular point in a particular period of time. Gas flow rate calculations are used extensively in the disciplines of chemical engineering and process engineering. Flow rate calculations through pipes are often challenging because pipes can vary in diameter along their length. The same basic calculations can be applied to any kind of gas.

Look at the reading of the pressure gauges at either end of the pipe. Pressure gauges consist of a circular dial with numbers marked around the edge. The pressure is indicated by the number to which the gauge arrow is pointing. Make a note of both of these values. Label the pressure at the beginning of the pipe as P1. Label the pressure at the end of the pipe as P2.

Place the two 'inside jaws' of the vernier calipers into the pipe and pull the two prongs apart until they are as far apart as they will go. The internal diameter of the pipe should be indicated on the scale on the side of the calipers. Label this value as D.

Calculate the cross sectional area of the pipe using the formula pi*(D/2)^2. What this formula means you divide your D value as determined in step 2 by 2, to give you the radius. You square the radius and multiply the resultant value by pi, or 3.1415. Make a note of the cross sectional area and label it as A.

Measure the length of the pipe using the tape measure. Make a note of this value and label it L.

Multiply the friction factor, f, of the interior surface of the pipe by the length, L, of the pipe. Divide this product by the diameter, D, of the pipe. Add the result of this calculation to 2 times the natural logarithm of P1 divided by P2. The natural logarithm can be determined by pressing the 'ln' key on a scientific calculator and entering the value of P1 divided by P2. Take this value and multiply it by the specific volume of the gas, v1. This value will be given in the engineering data book. Make a note of this value.

Divide the square of the cross sectional area of the pipe, A, by the value found in step 5. Make a note of this value.

Find the square of P2 and subtract it from the square of P1. Divide this value by the value of P1. Make a note of this value.

Multiply the value found and noted in step 6 by the value found and noted in step 7. Take the square of the product of these two values. This value is equal to the mass flow rate of the gas through the pipe.

#### Tip

Ensure that you use consistent units. If you measure the length of the pipe in inches, ensure that you measure the cross sectional area in square inches. The "specific volume" of a gas is the volume that a certain amount of that particular gas takes up. This value can be found for most common gases in any engineering or chemistry data book. The friction factor of the pipe is provided by the manufacturers of the pipe.

#### Tips and warnings

- Ensure that you use consistent units. If you measure the length of the pipe in inches, ensure that you measure the cross sectional area in square inches. The "specific volume" of a gas is the volume that a certain amount of that particular gas takes up. This value can be found for most common gases in any engineering or chemistry data book. The friction factor of the pipe is provided by the manufacturers of the pipe.

### Things you need

- Pressure gauges
- Vernier calipers
- Calculator
- Tape measure
- Engineering data book

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