Answer:
The force exerted on square meter of cubic sail is F = 15.3 N
Explanation:
Given:-
- The face area of cubic sail, A = 1 m^2
- The velocity at frontal face, v1 = 6.0 m/s
- The velocity at back face, v2 = 3.5 m/s
- The density of air. ρ = 1.29 kg/m^3
Find:-
Calculate the approximate force on a square meter (1.00 m3) of sail
Solution:-
- We will apply the Bernoulli's equation to the flow of air around the cubic sail. Assuming that elevation changes are negligible. The constant elevation Bernoulli's equation is:
P1 + ρ*v1^2 / 2 = P2 + ρ*v2^2 / 2
- The force (F) applied by any fluid is given by:
F = ( P2 - P1 )*A
- Re-arranging bernoulli's expression:
P2 - P1 = ρ/ 2 [ v2^2 - v1^2 ]
- Multiple the equation by area A:
A*[P2 - P1] = A*ρ/ 2 [ v1^2 - v2^2 ]
F = A*ρ/ 2 [ v1^2 - v2^2 ]
- Plug in the values:
F = (1)*(1.29/2)*[ 6^2 - 3.5^2 ]
F = 15.3 N
