Question

The force exerted on a bridge pier in a river is to be tested in a 1:10 scale model using water as the working fluid. In the prototype the depth of water is 2.0 m, the velocity of flow is 1.5 m/s and the width of the river is 20 m. Of the hydrodynamic force on the model bridge pier is 5 N, what would it be on the prototype? (hint: pressure ratio is equal to the length-scale ratio) (5 points; Ans: 5000 N)

Answer 1

Force on the prototype is 5000 N

Solution:

As per the question:

Depth of water, x = 2.0 m

Flow velocity, v' = 1.5 m/s

Width of the river, w = 20 m

Force on the bridge pier model, F' = 5 N

Pressure, Ratio = Ratio of scale length

Scale = 1:10

Now,

`(P')/(P) = (x)/(w) = (2.0)/(20)`

where

P' = pressure on model

P = pressure on prototype

`((F')/(A'))/((F)/(A)) = (1)/(10)`

where

F' = Force on model

F = Force on prototype

A' = Area of model

A = Area of prototype

Now:

`(F')/(F).(A)/(A') = (1)/(10)`

`(5)/(F).(1)/((1)/(10)).(1)/((1)/(10)) = (1)/(10)`

F = 5000 N