Final answer:
The net resultant force exerted on the reducer by the water is zero, as the momentum of the water is conserved.
Step-by-step explanation:
To determine the net resultant force exerted on the reducer by the water, we can make use of the momentum principle, which states that the change in momentum of an object is equal to the net force acting on it multiplied by the time interval over which the force is applied.
In this case, the water is flowing horizontally through a 25 cm-diameter pipe at 6 m/s and 300 kPa gage. It then enters a 90° bend reducing section, which connects to a 15 cm-diameter vertical pipe. Neglecting any frictional and gravitational effects, we can assume that the water's momentum is conserved. Therefore, the momentum before the bend reducing section is equal to the momentum after the bend reducing section.
The momentum of the water before the bend reducing section is given by:
M1 = ρ * A1 * V1
where ρ is the density of water, A1 is the cross-sectional area of the 25 cm-diameter pipe, and V1 is the velocity of the water.
Similarly, the momentum of the water after the bend reducing section is given by:
M2 = ρ * A2 * V2
where A2 is the cross-sectional area of the 15 cm-diameter vertical pipe and V2 is the velocity of the water after the bend.
Since the water's momentum is conserved, we can set M1 equal to M2:
ρ * A1 * V1 = ρ * A2 * V2
Cancelling out the density, we get:
A1 * V1 = A2 * V2
Since the pipe is horizontal and water is incompressible, the cross-sectional area remains constant along the horizontal and vertical sections. Therefore, A1 is equal to A2. This means that the velocity of the water after the bend reducing section, V2, is equal to the velocity of the water before the bend reducing section, V1.
Hence, the net resultant force exerted on the reducer by the water is zero, as the momentum of the water is conserved.