You are working as a summer intern for the Illinois Department of Natural Resources (DNR) and are assigned to some initial work on water resources project. The department will be overseeing the construction of a dam to create a large fresh water lake that will be approximately 14 meters deep. A horizontal pipe 1.2 meters long and 3 cm in diameter will pass through the dam at a depth of 7 meters to allow for release of the water in emergencies and for sampling. In normal situations, a plug will secure the pipe opening. 1)What will be the total force on the left side of the plug?FLEFT = N2)What is the total force on the right side of the plug?FRIGHT = N3)What is the gauge pressure on the plug?Pgauge = Pa4)If the plug were to be removed, how much water would flow out in 3 hours??VOL = m3

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

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.