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?
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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.
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