Math CentralQuandaries & Queries


Question from paul:

What is the volume of water in a 100mm inside diameter pipe that is 12.5 meters long
What would be the pressure at the bottom if the pipe was installed in the vertical plain


I am going to use centimeters for the units and hence your pipe has an inside diameter of 10 cm and is 1250 cm long. The volume of a cylinder is pi r2 h where r is the radius and h is the height. Thus the volume of water on your pipe is

pi 52 × 1250 = 98,178 cubic centimeters

or, if you prefer, 0.098179 cubic metres.

One cubic centimeter of water weighs one gram so the weight of the water is 98,178 grams which is 98.178 kilograms. If the pipe is vertical then the area of the water at the bottom of the pipe is

pi r2 = pi 52 = 78.54 square centimeters.

Hence the mass of water per unit area is

98.178/78.54 = 1.25 kg/cm2 = 1.25 ×104 kg/m2.

Pressure is measured as force per unit area and you have mass per unit area. To convert, we use F=ma, Newtons's second law. The a here is the acceleration due to gravity. So we simply multiply the figure above by the acceleration due to gravity (9.8 m/s2) and get 122.5 kPa (kiloPascals are each 103 kg / m / s2). This is the pressure due to the weight of the water, what is normally called "Gauge Pressure".

If you wanted absolute pressure instead of gauge pressure, you'd need to add the current atmospheric pressure to this. That's typically around another 100 kPa.

Although kPa are the normal metric units we use here in Canada, you may use torr or pounds per square inch. You can convert to such quantities (and many others) using the pressure converter at

Penny, Stephen and Gabe.

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