Question

Q=12nv2

The dynamic pressure q generated by a fluid moving with velocity v can be found using the formula above, where n is the constant density of the fluid. An aeronautical engineer users the formula to find the dynamic pressure of a fluid moving with velocity v and the same fluid moving with velocity 1.5v. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid?

Answer 1

The ratio is 2.25/1

Explanation:

Fluid 1

Q = 12 n v^2

Fluid 2

Q =12 n (1.5 v)^2

=12 n (2.25) v^2

Ratio of the faster fluid to the slower fluid

Fluid 2/Fluid 1

12 n (2.25) v^2

-----------------------

12 n v^2

Canceling 12 and n

(2.25) v^2

-----------------------

v^2

Canceling v^2

2.25

-------

1

The ratio is 2.25/1

Answer 2

Because V is raised to the second power in the original equation the velocity of the slower fluid is V^2.

The faster fluid is 1.5V, which when replaced in the equation becomes 1.5v^2.

The ratio would then be 1.5^2 which equals 2.25