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

Answer:

$f_p = 5000 N$

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

$\frac{p_m}{p_p} =\frac{l_m}{l_p} =\frac{1}{10}$

$\frac{f_m *A_m}{f_p *A_p} ==\frac{1}{10}$

$\frac{f_m}{f_p} * \frac{A_p}{A_m} = \frac{1}{10}$

$\frac{f_m}{f_p} * \frac{b_p*h_p}{b_m*h_m} =\frac{1}{10}$

$5 * \frac{1}{\frac{1}{10}} *\frac{1}{\frac{1}{10}} = \frac{f_p}{10}$

solving F_p

$f_p = 5000 N$