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# How to Calculate Forces & Moments on Nozzles

Updated July 20, 2017

Nozzles are mechanical devices which are used to control the flow or characteristics of fluids. Nozzles can come in many different shapes and forms; for example, nozzles can be used to increase thrust on a rocket, or to control the amount of fluid released from a pipe in a given amount of time. There can be many forces and moments that nozzles are subject to; however, the principles of calculating these forces and moments can be relatively straightforward.

Draw a free-body diagram, labelling all forces that potentially act on the nozzle. For example, on a horizontal nozzle releasing a fluid into the atmosphere, there are two opposing forces: the force due to the fluid from one direction, and the force due to the atmospheric pressure outside the nozzle from the other direction.

Determine the values of the labelled forces. In the example, there are two forces to consider. The fluid force is determined by dividing the pressure of the fluid by the area of the nozzle opening. As an example, assume the gauge pressure -- i.e., the pressure above atmospheric pressure -- is 3 bars, or equivalent to 300,000 pascals, a unit of measurement for pressure, subject to an area of 3 meters squared (m^2). The force acting on the nozzle is then 100,000 newtons, or N, the unit of measurement for force.

The force due to the atmospheric pressure is zero, since we measure the pressure of the fluid relative to the atmospheric pressure.

Calculate the resulting force. In our example, the resultant force is found by subtracting the force from the fluid by the atmospheric force; specifically, subtracting 100,000 N by 0 N gives 100,000 N. This is the force acting on the nozzle.

Draw a free-body diagram and determine the forces acting on the nozzle as before. For example, assume the resultant force is 150 N.

Label the dimensions of the nozzle and pipe and the location the forces act upon. For example, assume a force is applied completely vertically on the nozzle 2 meters from the start of the nozzle.

Calculate the moment by multiplying the distance at which the force acts on the nozzle by the force. In this specific example, multiplying 150 N by 2m results in 300 newton-meters, the unit of measurement for moments. This is the moment acting on the nozzle.