Answer:
(a) 120 kW
(b) 800 kW
Explanation:
Given:
diameter: 1.5 m
length = 22 m
U = 5 m/s
temperature = 20°C
For water at 20°C, take ρ = 998 kg/m³ and µ = 0.001 kg/m⋅s
To find:
power in kW
(a) if the cylinder is parallel
Length / Diameter = L / D = 22 / 1.5 = 14.6 = 15
Re(L) = ρ*U*L / µ = 998 * 5 * 22 / 0.001 = 109780000 = 1.1E8
C(D.Frontal) ≈ 1.1
Force = F = 1.1 * ρ/2 * U² * π / 4 * D
= 1.1 (998 / 2) (5)²(π / 4)(1.5)²
= 1.1 * 499 * 25 * 0.785 * 2.25
= 24000 N
Power = Force * Displacement / time
= F * U
= 24000 * 5
= 120000
Power = 120 kW
b) if the cylinder is normal to the tow direction.
Re(L) = ρ*U*D / µ = 998 * 5 * 1.5 / 0.001 = 7485000 = 7.5E6
C(D.Frontal) ≈ 0.4
Force = F = 0.4 * ρ/2 * U² * D * L
= 0.4 (998 / 2) (5)²(1.5)(22)
= 164670 ≈ 165000
Power = Force * Displacement / time
= F * U
= 165000 * 5 = 825000
≈ 800 kW
Power = 800 kW
