The water in the tank is 10 m above the leak point.The speed with which the water emerge from the leak is
Answers
Explanation:
As we showed in (Figure), when a fluid flows into a narrower channel, its speed increases. That means its kinetic energy also increases. The increased kinetic energy comes from the net work done on the fluid to push it into the channel. Also, if the fluid changes vertical position, work is done on the fluid by the gravitational force.
A pressure difference occurs when the channel narrows. This pressure difference results in a net force on the fluid because the pressure times the area equals the force, and this net force does work. Recall the work-energy theorem,
W
net
=
1
2
m
v
2
−
1
2
m
v
2
0
.
The net work done increases the fluid’s kinetic energy. As a result, the pressure drops in a rapidly moving fluid whether or not the fluid is confined to a tube.
There are many common examples of pressure dropping in rapidly moving fluids. For instance, shower curtains have a disagreeable habit of bulging into the shower stall when the shower is on. The reason is that the high-velocity stream of water and air creates a region of lower pressure inside the shower, whereas the pressure on the other side remains at the standard atmospheric pressure. This pressure difference results in a net force, pushing the curtain inward. Similarly, when a car passes a truck on the highway, the two vehicles seem to pull toward each other. The reason is the same: The high velocity of the air between the car and the truck creates a region of lower pressure between the vehicles, and they are pushed together by greater pressure on the outside ((Figure)). This effect was observed as far back as the mid-1800s, when it was found that trains passing in opposite directions tipped precariously toward one another.
Figure is an overhead view of a car passing a truck on a highway. Air passing between the vehicles flows in a narrower channel and increases the speed from v1 to v2, causing the pressure between vehicles to drop from Po to Pi.
Figure 14.29 An overhead view of a car passing a truck on a highway. Air passing between the vehicles flows in a narrower channel and must increase its speed (
v
2
is greater than
v
1
), causing the pressure between them to drop (
p
i
is less than
p
o
)
.
Greater pressure on the outside pushes the car and truck together.
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