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Solved: Show that the total force on a rectangular dam due
Chapter 11, Problem 23(choose chapter or problem)
Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by \(F=\rho g h^{2} L / 2\), where \(\rho\) is the density of water, \(h\) is its depth at the dam, and \(L\) is the length of the dam. You may assume the face of the dam is vertical. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water. (See Figure \(11.42\).)
Figure \(11.42\)
Equation Transcription:
Text Transcription:
F=rho gh^2 L/2
rho
h
L
11.42
Questions & Answers
QUESTION:
Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by \(F=\rho g h^{2} L / 2\), where \(\rho\) is the density of water, \(h\) is its depth at the dam, and \(L\) is the length of the dam. You may assume the face of the dam is vertical. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water. (See Figure \(11.42\).)
Figure \(11.42\)
Equation Transcription:
Text Transcription:
F=rho gh^2 L/2
rho
h
L
11.42
ANSWER:
Step 1 of 3
We have to calculate total force exerted by the water on rectangular dam.