Plz answer Provide computations and description to justify y

Provide computations and description to justify your results. No partial credit will be given for answers without justifying calculations or logic. A large (2 ft diameter inlet) valve is to tested for head loss with a 3 in inlet. scale model valve in a lab with water at the same temperature that the larger the big valve experiences is 30 ft^3/S. what is the largest flow at which the model should be tested?

Solution

For similarity, the model and the actual valve should both be tested at same Reynolds number.

Re = V*d / neu

Since both are tested in water, hence neu remains constant.

We get V₁*d₁ = V₂*d₂

Cross-section of large pipe A₁ = pi/4 * d1²

= 3.14 / 4 * 2²

A₁ = 3.14 ft²

Similarly, A₂ = 3.14/4 * (3/12)²

A₂ = 0.049 ft²

Velocity V₁ = Q₁ / A₁

= 30 / 3.14

V₁ = 9.554 ft/s

We get, 9.554 * 2 = V₂ * (3/12)

V₂ = 76.43 ft/s

Flowrate Q₂ = A₂*V₂

= 0.049 * 76.43

Q₂ = 3.745 ft³/s