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Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ________ N.

1. 350π²
2. 750π
3. 1000π

Correct answer: 750π

Solution

The force exerted by the gas on the pipe can be calculated using the momentum equation, which relates the change in momentum to the pressure drop and the area of the pipe. Given the increase in velocity and the pressure drop, the resulting force is determined to be 750π N, which corresponds to the net effect of the pressure and velocity changes in the flow.

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