Answer: CP CALC The upper edge of a gate in a dam runs

Chapter 12, Problem 54P

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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

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

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