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

ANSWER EXPLANATION: To solve this problem, you need to set up to equations with variables. Let q1 be the dynamic pressure of the slower fluid moving with velocity v1, and let q2 be the dynamic pressure of the faster fluid moving with velocity v2. Then

v2=1.5v1

Given the equation q=12nv2, substituting the dynamic pressure and velocity of the faster fluid gives q2=12n(v2)2. Since v2=1.5v1, the expression 1.5v1 can be substituted for v2 in this equation, giving q2=12n(1.5v1)2. By squaring 1.5, you can rewrite the previous equation as

q2=(2.25)(12)n(v1)2=(2.25)q1

Therefore, the ratio of the dynamic pressure of the faster fluid is

q2q1=2.25q1q1=2.25

The final answer is 2.25 or 9/4