A pressurised fluid passing through a narrow opening into a lower pressure environment increases velocity as it flows through the narrow opening. The density, according to the Venturi effect, decreases as the fluid passes through the opening. The mass flow eventually reaches a critical point at which it will not increase with a further drop in downstream pressure. That point is called the choked, or critical, flow point and it varies according to the size of the orifice through which the fluid flows. The orifice critical flow can produce a particular mass flow rate.
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Determine the specific heat ratio. The specific heat ratio is defined as the ratio between the heat capacity at a constant pressure divided by the heat capacity at a constant volume. Refer to a listing of specific heat capacities or specific heat ratios (see Resources).
Divide the sum of the specific heat plus one by two. Record the result. Divide the sum of the specific heat plus one by the product of two times the difference between the specific heat minus one. Record that result. Raise the first result to the negative power of the second result. For instance, if the specific heat were two, the first result equals two plus one divided by two, or three-halves. The second result equals two plus one divided by two times two minus one, or three-halves. Three-halves raised to the power of negative three-halves equals approximately 0.544.
Multiply the result by the square root of the specific heat divided by the gas constant R. Refer to a table of gas constant values (see Resources) for the appropriate R-value for your units of measurement. Record the product. For instance, if the specific heat were two and the R-value is 8.3144725 for jules per mole-Kelvin then the square root equals approximately 0.491, which multiplied by 0.544 equals approximate 0.267.
Calculate the cross-sectional area of the opening. Divide the diameter in half to determine its radius. Square the radius and multiply the result by pi. The result is the cross-sectional area of the opening. Use consistent measurement units throughout the equation and convert units when necessary.
Multiply the cross-sectional area of the opening by the total pressure. Divide the product by the total temperature. Multiply the result by the result determined previously to calculate mass flow rate at the orifice critical flow. For instance, if the cross sectional area of the opening were 3 square meters, the total pressure were 500 pascals and the total temperature were 300 Kelvins then the result would be 5 square meter-pascals per Kelvin. Multiplied by the previous result equals 1.335 kilograms per second.
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