Final answer:
To calculate the horizontal and vertical anchoring forces required to hold the elbow in place, we can use the principle of conservation of momentum. The horizontal force is zero since the elbow is at rest, but the vertical anchoring force can be calculated using the density of water and the volume flow rate.
Step-by-step explanation:
To calculate the horizontal and vertical anchoring forces required to hold the elbow in place, we can use the principle of conservation of momentum.
First, let's calculate the change in momentum of the water as it flows through the elbow. The initial momentum can be calculated as:
P1 = m1 * v1
Where m1 is the mass of the water at the inlet and v1 is its velocity. Similarly, the final momentum can be calculated as:
P2 = m2 * v2
Where m2 is the mass of the water at the outlet and v2 is its velocity. Since the elbow is at rest, the change in momentum is equal to zero:
P2 - P1 = 0
Substituting the values, we can find the velocities:
(m2 * v2) - (m1 * v1) = 0
We can re-arrange the equation to solve for v2:
v2 = (m1 * v1) / m2
Using the given values, we find that the velocity at the outlet is v2 = 2 * v1.
Now, let's calculate the horizontal and vertical anchoring forces. The horizontal force can be calculated using the equation:
Fhorizontal = m * ahorizontal
Where m is the mass of the water and ahorizontal is the acceleration in the horizontal direction. Since the elbow is at rest, the horizontal force is equal to zero:
Fhorizontal = 0
The vertical force can be calculated using the equation:
Fvertical = m * avertical
Where avertical is the acceleration in the vertical direction. Substituting the values, we find that:
Fvertical = m * g
Where g is the acceleration due to gravity. Using the given mass of the elbow, we can calculate the vertical anchoring force. Since we know the density of water, we can calculate its mass using the volume flow rate:
m = ρ * V = ρ * A * v
Substituting the values, we find that:
Fvertical = (ρ * A * v) * g
Using the given values, we find that the vertical anchoring force is Fvertical = 117.6 N.