Question

If the specific heat ratio of natural gas is 1.28, the critical pressure ratio (ratio of outlet pressure to upstream pressure) through a choke is \(\underline{\hspace{2cm}}\) (round off to two decimal places).

Hint:

The critical pressure ratio is an important parameter in flow through chokes, especially when dealing with compressible fluids like natural gas.

Answer 1

Correct Answer: 0.52

The critical pressure ratio for choking flow is given by the formula:
\[ \left( \frac{P_{out}}{P_{in}} \right)_{cr} = \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}} \] Where \( \gamma = 1.28 \) is the specific heat ratio. Substituting the value of \( \gamma \):
\[ \left( \frac{P_{out}}{P_{in}} \right)_{cr} = \left( \frac{2}{1.28 + 1} \right)^{\frac{1.28}{1.28 - 1}} = \left( \frac{2}{2.28} \right)^{\frac{1.28}{0.28}} = (0.877)^{4.571} \] Approximating the value:
\[ \left( \frac{P_{out}}{P_{in}} \right)_{cr} \approx 0.522 \] Thus, the critical pressure ratio is \( \boxed{0.52} \).