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Pra_S

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Hi,

Case 1:

Imagine a steady liquid water jet with unit cross sectional area - incompressible and inviscid. density D and uniform velocity V. Operating atmospheric pressure is 0.0 Pa.

The jet is in air ( no air resistance ) and hits a stationary flat plate perpendicularly.

Applying momentum equation gives - the force on the plate by the water jet as : D*V*V = DVV.

Hence the pressure on the plate = DVV / Area = DVV. (Area = 1)

Case 2.

For the same scenario the Stagnation pressure is = 0.5*D*V*V = 0.5 D V^2

The stagnation pressure is the pressure just before the plate, when the fluid completely stops on impact.

However, the two answers are different.

I have read the followings in the literature.

1. In practice, when the water first hit the plate it creates very high pressure (water hammer), which lasts for few micro seconds.

2. Then the pressure reduces and settles at the stagnation pressure.

My question is:

What quantity ( relevance in practice) is calculated using the momentum equation.

PS. - I have seen that , the initial water hammer on the plate can be calculated by Density*V*Speed of sound in water. Which is different than what is estimated though the momentum equation.

Case 1:

Imagine a steady liquid water jet with unit cross sectional area - incompressible and inviscid. density D and uniform velocity V. Operating atmospheric pressure is 0.0 Pa.

The jet is in air ( no air resistance ) and hits a stationary flat plate perpendicularly.

Applying momentum equation gives - the force on the plate by the water jet as : D*V*V = DVV.

Hence the pressure on the plate = DVV / Area = DVV. (Area = 1)

Case 2.

For the same scenario the Stagnation pressure is = 0.5*D*V*V = 0.5 D V^2

The stagnation pressure is the pressure just before the plate, when the fluid completely stops on impact.

However, the two answers are different.

I have read the followings in the literature.

1. In practice, when the water first hit the plate it creates very high pressure (water hammer), which lasts for few micro seconds.

2. Then the pressure reduces and settles at the stagnation pressure.

My question is:

What quantity ( relevance in practice) is calculated using the momentum equation.

PS. - I have seen that , the initial water hammer on the plate can be calculated by Density*V*Speed of sound in water. Which is different than what is estimated though the momentum equation.

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