Q = 1/2 nv2 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?
SAT · High School · Wed Jan 13 2021
Answered on
The dynamic pressure q for a fluid moving with velocity v can be found using the formula q = (1/2) * n * v². Let's calculate the dynamic pressure for two different velocities: v and 1.5v.
1. For velocity v, the dynamic pressure is q₁ = (1/2) * n * v². 2. For velocity 1.5v, the dynamic pressure is q₂ = (1/2) * n * (1.5v)² = (1/2) * n * 2.25v².
Next, let's find the ratio of q₂ to q₁:
q₂/q₁ = [(1/2) * n * 2.25v²] / [(1/2) * n * v²]
Since (1/2) * n is a common factor, it cancels out, and we get:
q₂/q₁ = 2.25v² / v²
This simplifies to:
q₂/q₁ = 2.25
Therefore, the ratio of the dynamic pressure of the fluid moving with velocity 1.5v to that of the fluid moving with velocity v is 2.25:1.