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Answer :
Answer:
7.404 psi
Explanation:
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Final answer:
To determine the total pressure drop across the plumbing branch, we can use the Darcy-Weisbach equation and consider factors such as the pipe length, diameter, flow rate, and type of fittings. In this case, the pressure drop is approximately 219.4 psi.
Explanation:
To determine the total pressure drop across the plumbing branch, we need to consider the pressure drop due to the length of the pipe, the elbows, and the gate valve. The pressure drop in a pipe is given by the Darcy-Weisbach equation, which takes into account factors such as the pipe diameter, flow rate, and pipe roughness. In this case, we can assume that the pipe is smooth and the flow is turbulent, so we can use the simplified version of the equation:
dP = 0.2083 * (L/D) * (V^2 / 2g)
where dP is the pressure drop in psi, L is the pipe length in feet, D is the pipe diameter in inches, V is the flow velocity in ft/s, and g is the acceleration due to gravity (32.2 ft/s^2).
Using the given values, we can calculate the pressure drop:
- Convert the pipe length to inches: 68' * 12 = 816".
- Calculate the flow velocity: 45 gpm = (45 * 144) / (60 * A) ft/s, where A is the cross-sectional area of the pipe in square inches. For a 1" diameter pipe, the area is approximately 0.7854 square inches. Substituting the values, we get V ≈ 4.545 ft/s.
- Substitute the values into the equation: dP = 0.2083 * (816 / 1) * (4.545^2 / 2 * 32.2).
- Calculate the pressure drop: dP ≈ 219.4 psi.
Therefore, the total pressure drop across the plumbing branch is approximately 219.4 psi.
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