Choked Flow Pressure Calculator

Calculate Choked Flow Pressure (P_c)



Formula

The formula to calculate the Choked Flow Pressure (P_c) is:

\[ P_c = P_u \cdot \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}} \]

Where:

Example

Let's say the upstream pressure (\( P_u \)) is 100,000 Pa and the specific heat ratio (\( k \)) is 1.4. Using the formula:

\[ P_c = 100,000 \cdot \left(\frac{2}{1.4+1}\right)^{\frac{1.4}{1.4-1}} \]

We get:

\[ P_c = 100,000 \cdot \left(\frac{2}{2.4}\right)^{3.5} \approx 52,828 \text{ Pa} \]

So, the Choked Flow Pressure (\( P_c \)) is approximately 52,828 Pa.

What is Choked Flow Pressure?

Choked flow pressure is a condition in fluid dynamics where the flow rate of a compressible fluid through a restriction does not increase with a further decrease in downstream pressure. This occurs when the velocity of the fluid reaches the speed of sound in the fluid at the narrowest point of the restriction. Choked flow is significant in various engineering applications, including the design of nozzles, valves, and other components where controlling the flow rate of gases is critical.

Extended information about "Choked-Flow-Pressure-Calculator"

Gas Choked Flow Calculator

Definition: Calculate the choked flow of gas through a nozzle or orifice.

Formula: \( \dot{m} = C_d A \sqrt{\frac{2 \rho \Delta P}{1 - \left(\frac{P_2}{P_1}\right)^{\frac{2}{\gamma}}}} \)

Example: \( \dot{m} = 0.8 \times 0.01 \sqrt{\frac{2 \times 1.2 \times 100}{1 - \left(\frac{50}{100}\right)^{\frac{2}{1.4}}}} \)

Choked Mass Flow Rate Calculator

Definition: Calculate the choked mass flow rate of a gas.

Formula: \( \dot{m} = C_d A P_1 \sqrt{\frac{\gamma}{R T_1} \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{\gamma - 1}}} \)

Example: \( \dot{m} = 0.9 \times 0.02 \times 100 \sqrt{\frac{1.4}{287 \times 300} \left(\frac{2}{1.4 + 1}\right)^{\frac{1.4 + 1}{1.4 - 1}}} \)

Critical Pressure Ratio Choked Flow

Definition: Calculate the critical pressure ratio for choked flow.

Formula: \( \frac{P_2}{P_1} = \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma}{\gamma - 1}} \)

Example: \( \frac{P_2}{P_1} = \left(\frac{2}{1.4 + 1}\right)^{\frac{1.4}{1.4 - 1}} \)

Choked Gas Flow Equation

Definition: Calculate the choked gas flow through a nozzle or orifice.

Formula: \( \dot{m} = C_d A P_1 \sqrt{\frac{\gamma}{R T_1} \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{\gamma - 1}}} \)

Example: \( \dot{m} = 0.85 \times 0.015 \times 120 \sqrt{\frac{1.4}{287 \times 310} \left(\frac{2}{1.4 + 1}\right)^{\frac{1.4 + 1}{1.4 - 1}}} \)

Choked Flow Orifice Calculator

Definition: Calculate the choked flow through an orifice.

Formula: \( \dot{m} = C_d A P_1 \sqrt{\frac{\gamma}{R T_1} \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{\gamma - 1}}} \)

Example: \( \dot{m} = 0.75 \times 0.01 \times 110 \sqrt{\frac{1.4}{287 \times 290} \left(\frac{2}{1.4 + 1}\right)^{\frac{1.4 + 1}{1.4 - 1}}} \)