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The important parameters describing the performance of a hydraulic machine are: P the power input, H the head produced across the machine and the efficiency, η. For a given geometrical design of the machine, the performance is characterized by the variables: H – the head increase across the machine ρ – the fluid density, ω – the angular velocity of the rotor, D – the diameter of the rotor, μ  – the fluid viscosity and Q – the flow rate; and both P and η are expressed through these variables. How many non-dimensional parameters are involved herein? Gravitational acceleration g has also to be considered necessarily?

The important parameters describing the performance of a hydraulic machine are: P the power input, H the head produced across the machine and the efficiency, η. For a given geometrical design of the machine, the performance is characterized by the variables: H – the head increase across the machine ρ – the fluid density, ω – the angular velocity of the rotor, D – the diameter of the rotor, μ  – the fluid viscosity and Q – the flow rate; and both P and η are expressed through these variables. How many non-dimensional parameters are involved herein? Gravitational acceleration g has also to be considered necessarily? Correct Answer 4

P and η can be expressed in terms of 7 parameters - H, ρ, ω, D, μ, Q, g.

No. of non dimensional parameter = Total parameters – total fundamental parameters involved in given situation

Fundamental parameters are generally 3 in Number and they include dimensions of length, mass and time.

If we observe carefully all above 7 parameters, we got all 3 fundamental parameters.

 For instance, density is mass per unit volume, it has dimension of Mass and length. Similarly, acceleration due to gravity has dimension of distance and time. By combining all these, we got all 3 fundamental parameters in above given situation.

∴ Non dimensional parameter = 7 - 3 = 4.

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