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Specific total-enthalpy change follows from blade speed and tangential absolute velocity at inlet and outlet.
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Formula
Δh0 in J/kg; U and Cθ in m/s
| Symbol | Meaning | Unit |
|---|---|---|
| Specific total-enthalpy change | J/kg | |
| Blade peripheral speeds at inlet and outlet | m/s | |
| Tangential absolute-flow velocity components | m/s |
\Delta h_0=U_2C_{\theta2}-U_1C_{\theta1}This is the steady angular-momentum balance per unit mass under a chosen sign convention. Signs for work transfer depend on turbine or compressor direction and velocity triangles. Losses, nonuniform flow and radial distributions require efficiency and correction models.
This is the steady angular-momentum balance per unit mass under a chosen sign convention. Signs for work transfer depend on turbine or compressor direction and velocity triangles. Losses, nonuniform flow and radial distributions require efficiency and correction models.
Specific total-enthalpy change follows from blade speed and tangential absolute velocity at inlet and outlet.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Euler turbomachinery equation” and check its unit and magnitude.
For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Δh0 in J/kg; U and Cθ in m/s.
Formula cluster
Specific total-enthalpy change follows from blade speed and tangential absolute velocity at inlet and outlet.
For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg.
Relate work transfer and swirl change in turbines and compressors.
Here is how to work through a typical Euler turbomachinery equation (Δh₀ = U₂Cθ₂ − U₁Cθ₁) task step by step:
Task
Work through the numerical example for “Euler turbomachinery equation” and check its unit and magnitude.
Solution path
For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg.
Cθ is the tangential component of absolute fluid velocity at the rotor section. It differs from blade speed U. Their product represents the specific angular-momentum contribution to energy transfer. Keep velocity-triangle directions and turbine/compressor sign convention consistent. Application: Relate work transfer and swirl change in turbines and compressors. The numerical example For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg anchors the idea in a concrete measurement case. The corresponding units are Δh0 in J/kg; U and Cθ in m/s. For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg. This checks that the reference quantities are compatible.
Turbines and compressors transfer energy in opposite directions. Depending on convention, Δh0 may mean fluid enthalpy rise or shaft work output. Define directions of U, swirl and enthalpy change before interpreting sign. Keep velocity-triangle directions and turbine/compressor sign convention consistent. The corresponding units are Δh0 in J/kg; U and Cθ in m/s. For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg. This checks that the reference quantities are compatible. Scope: This is the steady angular-momentum balance per unit mass under a chosen sign convention. Signs for work transfer depend on turbine or compressor direction and velocity triangles. Losses, nonuniform flow and radial distributions require efficiency and correction models. A practical application is Relate work transfer and swirl change in turbines and compressors.
It gives work from angular momentum and remains a core stage relation, but real states include friction, leakage and mixing losses. Efficiency and actual outlet states need separate modeling; ideal Euler work is not automatically useful shaft output. Keep velocity-triangle directions and turbine/compressor sign convention consistent. Scope: This is the steady angular-momentum balance per unit mass under a chosen sign convention. Signs for work transfer depend on turbine or compressor direction and velocity triangles. Losses, nonuniform flow and radial distributions require efficiency and correction models. A practical application is Relate work transfer and swirl change in turbines and compressors.
Write the quantity and unit from the variable list next to every value: Δh0 in J/kg; U and Cθ in m/s. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For U1=100 m/s, Cθ1=20 m/s, U2=200 m/s, Cθ2=120 m/s, the stated convention gives Δh0=22 kJ/kg. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Keep velocity-triangle directions and turbine/compressor sign convention consistent.
The background states this starting condition: This is the steady angular-momentum balance per unit mass under a chosen sign convention. Signs for work transfer. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Keep velocity-triangle directions and turbine/compressor sign convention consistent.
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Curated exam set for "Euler turbomachinery equation":
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Which formula describes Euler turbomachinery equation?
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Question (front)
How do you rearrange Euler turbomachinery equation for Base equation for the target quantity?
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Which common mistake happens with Euler turbomachinery equation?
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Create a curated FSRS exam set for Δh₀ = U₂Cθ₂ − U₁Cθ₁: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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