A closed and elevated vertical cylindrical tank withdiameter 2.00 m contains water to a depth of 0.800 m. A worker accidentlypokes a circular hole with diameter 0.0200 m in the bottom of thetank. As the water drains from the tank, compressed air above the waterin the tank maintains a gauge pressure of 5.00 * 10^3 Pa at the surface ofthe water. Ignore any effects of viscosity. (a) Just after the hole is made,what is the speed of the water as it emerges from the hole? What is theratio of this speed to the efflux speed if the top of the tank is open tothe air? (b) How much time does it take for all the water to drain fromthe tank? What is the ratio of this time to the time it takes for the tank todrain if the top of the tank is open to the air?
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
A closed and elevated vertical cylindrical tank with
diameter 2.00 m contains water to a depth of 0.800 m. A worker accidently
pokes a circular hole with diameter 0.0200 m in the bottom of the
tank. As the water drains from the tank, compressed air above the water
in the tank maintains a gauge pressure of 5.00 * 10^3 Pa at the surface of
the water. Ignore any effects of viscosity. (a) Just after the hole is made,
what is the speed of the water as it emerges from the hole? What is the
ratio of this speed to the efflux speed if the top of the tank is open to
the air? (b) How much time does it take for all the water to drain from
the tank? What is the ratio of this time to the time it takes for the tank to
drain if the top of the tank is open to the air?
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