Question

The inlet and exit flow conditions of a subsonic diffuser are shown. The diffuser has an area ratio of A2​/A1​= 1.25. Assuming the fluid is air and is treated as a calorically perfect gas with γ=1.4 and R=287 J/Kg⋅K, calculate (a) the mass flow rate in kg/s (b) the exit Mach number M2​ (c) the diffuser static pressure recovery CPR​≡ (p2​−p1​)/q1​ (d) the axial force exerted on the diffuser wall by the fluid in kN

Answer 1

To find the mass flow rate, use the equation mdot = rho * A * V. The exit Mach number can be calculated using M2 = sqrt((2/(gamma-1)) * ((P1/P2)^((gamma-1)/gamma) - 1)). The diffuser static pressure recovery is given by CPR = (P2 - P1) / (0.5 * rho1 * V1^2). The axial force exerted on the diffuser wall is F = mdot * (V2 - V1).

Step-by-step explanation:

To calculate the mass flow rate in kg/s, we can use the equation:

mdot = rho * A * V

Where:

• mdot is the mass flow rate
• rho is the density of the fluid
• A is the cross-sectional area
• V is the velocity of the fluid

Given the area ratio A2/A1=1.25 and the inlet flow conditions, we can use the mass flow rate equation to find the mass flow rate.

For the exit Mach number M2, we can use the isentropic flow relations:

M2 = sqrt((2/(gamma-1)) * ((P1/P2)^((gamma-1)/gamma) - 1))

Where:

• M2 is the exit Mach number
• gamma is the specific heat ratio
• P1 is the inlet static pressure
• P2 is the exit static pressure

To calculate the diffuser static pressure recovery CPR, we can use the equation:

CPR = (P2 - P1) / (0.5 * rho1 * V1^2)

Where:

• P1 is the inlet static pressure
• P2 is the exit static pressure
• rho1 is the inlet density
• V1 is the inlet velocity

Finally, to calculate the axial force exerted on the diffuser wall, we can use the equation:

F = mdot * (V2 - V1)

Where:

• F is the axial force
• mdot is the mass flow rate
• V1 is the inlet velocity
• V2 is the exit velocity