Question

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/m\(^3\) 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.

• A. \( 350\pi \)
• B. \( 750\pi \)
• C. \( 1000\pi \)

Hint:

The force exerted by a compressible fluid in a pipe can be calculated using the pressure difference and the cross-sectional area of the pipe.

Answer 1

The Correct Option is B

Step 1: Use the equation for force exerted by gas.
The force exerted by the gas can be calculated using the equation \[ F = \Delta P \cdot A, \] where \( \Delta P \) is the pressure drop and \( A \) is the cross-sectional area of the pipe. Step 2: Calculate the cross-sectional area.
The area of the pipe is given by \[ A = \frac{\pi d^2}{4}, \] where \( d \) is the diameter of the pipe (1 m). Step 3: Calculate the force.
Substitute the values for \( \Delta P \) and \( A \) into the equation to calculate the force. Final Answer: \[ \boxed{750\pi} \]