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. If 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

`f_p = 5000 N`

Step-by-step explanation:

GIVEN DATA:

pressure ratio = length ratio

force = 5 N

scale = 1:10

velocity = 1.5 m/s

`B_p = 20 m`

`h_p = 2m`

As pressure ratio = length ratio so we have

`(p_m)/(p_p) =(l_m)/(l_p) =(1)/(10)`

`(f_m *A_m)/(f_p *A_p) ==(1)/(10)`

`(f_m)/(f_p) * (A_p)/(A_m) = (1)/(10)`

`(f_m)/(f_p) * (b_p*h_p)/(b_m*h_m) =(1)/(10)`

`5 * (1)/((1)/(10)) *(1)/((1)/(10)) = (f_p)/(10)`

solving F_p

`f_p = 5000 N`