Physics 23

Fluid Mechanics

1.Force on a dam. A dam has a height H and a width W.

The water behind the dam is at a height H.

a.Find the gauge pressure on the dam at a height y above the bottom due to the water behind the dam.

b.In order to find the total force on the dam due to the water, we cannot take the pressure found in part (a) and multiply it by the area (H x W) of the face of the dam (i.e., force = pressure x area). Why not?

c.Find the total force on the dam due to the water.

d.Which dam has a greater force on it due to the water behind it? Explain.

2.Suppose you are in a boat floating on a lake. Inside the boat is a block of wood and a steel anchor. You throw the block of wood overboard into the water.

a.Will the bloat float higher in the water, lower in the water, or remain floating at the same height? Explain.

b.Does the water level in the lake rise, fall, or remain the same? Explain.

You now throw the anchor overboard into the water. The anchor sinks to the bottom of the lake and is not attached to the boat.

c.Will the boat float higher in the water, lower in the water, or remain floating at the same height compared to before the anchor was thrown overboard? Explain.

b.Does the level of the water in the lake rise, fall, or remain the same compared to before the anchor was thrown overboard? Explain.

3.An ice cube (ice = 0.917 g/cm3) is floating in a cup of water (water = 1.00 g/cm3). After the ice cube melts, will the level of the water in the cup be higher than, lower than, or remain the same as before? Explain.

4.A solid styrofoamsphere (st = 0.25 g/cm3) with a radius of 20 cm is floating in seawater (sw = 1.034 g/cm3).

a.What mass of aluminum (Al = 2.70 g/cm3) must be balanced on top of the sphere so that half of the sphere is submerged in the water?

b.What mass of aluminum must be suspended from the bottom of the sphere in order for the sphere to be completely submerged in the water?

5.A large, sealed container resting on the ground is filled with water (w = 1.00 g/cm3) to a height of 90 cm. Air is pumped into the space above the surface of the water to a gauge pressure of 0.65 x 105Pa. A small hole, one centimeter in diameter, is made in the side of the container 35 cm below the surface of the water. What is the flow rate of the water coming out of the hole in m3/sec? How far from the side of the container will the water hit the ground?