- #1

MysticDream

- 80

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- TL;DR Summary
- Trying to understand Euler's turbine equation and velocity triangles.

I'm having a difficult time understanding Euler's turbine equation as it relates to designing a centrifugal air compressor. I need to calculate the impeller size if I know the inlet pressure, outlet pressure, rpm, and mass flow rate. The velocity triangles and definitions have me confused. It's the exit velocity of the air that I need to determine.

I have this equation for rate of work (power) from Euler's turbine equation:

$$P = \dot m(u_2c_2-u_1c_1)$$

where

u = tangential velocity of the impeller at inlet and outlet

c = absolute velocity of the fluid at inlet and outlet

I know I can use the formula for adiabatic compression to determine the power if I know the inlet volumetric flow rate, inlet pressure, outlet pressure, and RPM:

$$P = \left( \frac{(V_1P_1-V_2P_2)}{(\gamma-1)}\right)\left(\frac{RPM}{60}\right)$$

That leaves me with two variables in the first equation that I don't know, the absolute velocity of the air at the inlet and outlet. If the cross sectional area between the blades was constant (in say a tapered impeller), wouldn't the absolute velocity of the gas be the same at inlet and outlet? I know I can make variables "u" whatever I want by changing the internal and external diameter of the impeller until I get the desired exit gas velocity.

If there is another strategy to solve this problem, I'd like to know. If anyone has any insight to offer, I'd greatly appreciate it.

I have this equation for rate of work (power) from Euler's turbine equation:

$$P = \dot m(u_2c_2-u_1c_1)$$

where

u = tangential velocity of the impeller at inlet and outlet

c = absolute velocity of the fluid at inlet and outlet

I know I can use the formula for adiabatic compression to determine the power if I know the inlet volumetric flow rate, inlet pressure, outlet pressure, and RPM:

$$P = \left( \frac{(V_1P_1-V_2P_2)}{(\gamma-1)}\right)\left(\frac{RPM}{60}\right)$$

That leaves me with two variables in the first equation that I don't know, the absolute velocity of the air at the inlet and outlet. If the cross sectional area between the blades was constant (in say a tapered impeller), wouldn't the absolute velocity of the gas be the same at inlet and outlet? I know I can make variables "u" whatever I want by changing the internal and external diameter of the impeller until I get the desired exit gas velocity.

If there is another strategy to solve this problem, I'd like to know. If anyone has any insight to offer, I'd greatly appreciate it.