Answer:
1) F = 71.6 N
, 2) F = 120.2 N
, 3) P_m= 68.600 Pa, 4) V = 2.4210-5 m³
Explanation:
This is a problem of fluid mechanics, to find the force we must use its definition
P = F / A
F = P A
The area of the circular pipe is
A = π r² = π d²/4
The pressure is given by the expression
P = P_atm + ρ g h
1) the force on the outer side is
P = P_atm
we substitute in the expression of force
F = P_atm π d² / 4
let's calculate
F = 1,013 10⁵ π 0.03²/4
F = 7.16 10¹ N
F = 71.6 N
2) the force on the inner side
the pressure
P = P_atm + ρ g h
P = 1,015 10⁵ + 1,000 9.8 7
P = 1,701 10⁵ Pa
F = 1,701 10⁵ π 0.03² / 4
F = 1,202 10²
F = 120.2 N
3) manometric pressure
Pm = ρ g h
P m = 1000 9.8 7
P_m= 68.600 Pa
4) In this part they ask for the volume that comes out in time t= 3 h
to calculate this volume we can use the flow ratio
Q = A v
V t = A v
V = A v / t
sent is the velocity of the water that comes out, to calculate it we use the Bernoulli equation
we will use index 1 for the lake surface and ionice 2 apa the position of the plug
P₁ + ρ g v₁² + ρ g y₁ = P₂ + ρ g v₂² + ρ g y₂
As the lake has much more capacity than the pipeline, the velocity of the surface of the lake is peeling, in this case we approximate it steel
(P₁-P₂) + ρ G (y₁ -y₂) = ρ g v₂²
1000 9.8 v₂² = ρ g h + 1000 9.8 (7-0)
9800 v₂² = 1000 9.8 7 + 68600
v₂ = √ (137200)
v₂ = 370.4 m / s
t = 3 h (3600s / h) = 10800 s
we substitute in the volume equation
V = π d²/4 370.4 / 10800
V = 2.4210-5 m³
