Question

A reducing elbow in a horizontal pipe is used to deflect water flow by an angle theta = 45 degree from the flow direction while accelerating it. The elbow discharges water into the atmosphere. The cross-sectional area of the elbow is 150 cm2 at the inlet and 25 cm2 at the exit. The elevation difference between the centers of the exit and the inlet is 40 cm The mass of the elbow and the water in it is 50 kg. Determine the anchoring force needed to hold the elbow in place.

Answer 1

To determine the anchoring force needed to hold the elbow in place, we need to consider the forces acting on the system. The force due to the change in momentum can be calculated using the principle of conservation of momentum. The anchoring force needed to hold the elbow in place is the sum of the force due to the change in momentum and the weight of the water.

Step-by-step explanation:

To determine the anchoring force needed to hold the elbow in place, we need to consider the forces acting on the system. Since the water is accelerating, there must be an unbalanced force acting on it. This unbalanced force is the resultant of the forces due to the change in momentum and the weight of the water.

The force due to the change in momentum can be calculated using the principle of conservation of momentum. The change in momentum is equal to the mass of water entering the elbow multiplied by the change in velocity (v) and the cross-sectional area of the elbow at the inlet. The weight of the water is equal to the mass of water multiplied by the acceleration due to gravity.

The anchoring force needed to hold the elbow in place is the sum of the force due to the change in momentum and the weight of the water. This force can be calculated using the equation:

Force = (Δp) / t + (m * g)

where Δp is the change in momentum, t is the time it takes for the water to pass through the elbow, m is the mass of the water, and g is the acceleration due to gravity.