Solution Found!
Answer: CP CALC The upper edge of a gate in a dam runs
Chapter 12, Problem 54P(choose chapter or problem)
The upper edge of a gate in a dam runs along the water surface. The gate is \(2.00 \mathrm{~m}\) high and \(4.00 \mathrm{~m}\) wide and is hinged along a horizontal line through its center (Fig. P12.54). Calculate the torque about the hinge arising from the force due to the water. (Hint: Use a procedure similar to that used in Problem 12.53; calculate the torque on a thin, horizontal strip at a depth h and integrate this over the gate.)
Equation Transcription:
Text Transcription:
2.00 m
4.00 m
Questions & Answers
QUESTION:
The upper edge of a gate in a dam runs along the water surface. The gate is \(2.00 \mathrm{~m}\) high and \(4.00 \mathrm{~m}\) wide and is hinged along a horizontal line through its center (Fig. P12.54). Calculate the torque about the hinge arising from the force due to the water. (Hint: Use a procedure similar to that used in Problem 12.53; calculate the torque on a thin, horizontal strip at a depth h and integrate this over the gate.)
Equation Transcription:
Text Transcription:
2.00 m
4.00 m
ANSWER:
Solution 54P
Step 1:
Pressure of the water column, P = 𝜌gh
Where, 𝜌 - Density of water
g - Acceleration due to gravity
h - Height of the water column
Equation for force, F = PA
Where, P - Pressure acting on the surface
A - Area of the surface
Then, for an elemental area dA, the force acting, dF = PdA