Fluids: A stationary object in a flow of speed 5 m/s produces a drag force of 3 N. The flow speed is then changed to 25 m/s. What will be the drag force if the Drag Coefficient and density are assumed constant. Give your answer to two decimal places.

Question

Fluids: A stationary object in a flow of speed 5 m/s produces a drag force of 3 N. The flow speed is then changed to 25 m/s. What will be the drag force if the Drag Coefficient and density are assumed constant. Give your answer to two decimal places.

BlackTom AI · Accepted Answer

We start from the relationship for drag in a flow when Cd, ρ, and A are constant: F_drag ∝ v^2.

Given F_drag1 = 3 N at v1 = 5 m/s, and the new flow speed v2 = 25 m/s, we can compare the forces via the square of the speeds:

F_drag2 = F_drag1 × (v2^2 / v1^2).

Compute the squares: v2^2 = 25^2 = 625, v1^2 = 5^2 = 25.

Then F_drag2 = 3 N × (625 / 25) = 3 N × 25 = 75.00 N.

So, the drag force scales with the square of the speed, and increasing speed from 5 m/s to 25 m/s (a factor of 5) increases the drag by a factor of 25, yielding 75.00 N.

Key idea: proportionality of drag to velocity squared, and independence from Cd, ρ, and A when held constant.

Engineering Science B 2024 Progress Test 3 Progress Test 3

Fluids: A stationary object in a flow of speed 5 m/s produces a drag force of 3 N. The flow speed is then changed to 25 m/s. What will be the drag force if the Drag Coefficient and density are assumed constant. Give your answer to two decimal places.

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