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 ? ? ?gh2?L/ 2 ,?where ?? is the density of ?wate? is its depth at the da? , and? 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.)
Step-by-step solution Step 1 of 5 Formula is used to find pressure due to the weight of fluid. It can also be used to determine the force or pressure exerted on the face of a damp. Step 2 of 5 Refer to the figure 11.42 provided in the textbook. The pressure due to the weight of fluid is, …… (1) Here, is pressure, is the depth, is density and g is gravity. Step 3 of 5 From the figure11.42, average height of the water behind the dam is . So the average pressure on the dam is, …… (2) From definition of pressure, …… (3) Here, is pressure, is the applied force and is area perpendicular to the force.