A bucket is filled with water to a height of , then a plug is removed from a hole in the bottom of the bucket. As the water begins to pour out of the hole, how fast is it moving
The speed of water flowing out of the hole is .
The expression for Bernoulli's equation for a flowing fluid, between two points and is written as,
Here, is the pressure at point , is the pressure at point , is the velocity at point , is the velocity at point , is the position of point above the datum, is the position of point above the datum and is the density of the flowing fluid.
Continuity equation between the above mentioned points is written as,
Here, and are the cross-sectional areas of the flow at the points and , respectively.
Understand that point is the top of the bucket and the point is at the hole. The height is measured from the top of the bucket. The pressure at points and is atmospheric pressure. So,
Here, is atmospheric pressure.
It is known that area of hole is much smaller to the area of water at the top of the bucket. Hence,
Apply continuity equation between points and
Use equations and , to get:
Squaring both sides of the equation.
Hence can be neglected.
Substitute for and, for and for .
Substitute for and for ,
A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. When in equilibrium, what length of the cylinder is submerged?
An aquarium of length , width (front to back) , and depth is filled to the top with liquid of density
a. Find an expression for the force of the liquid on the bottom of the aquarium.
b. Find an expression for the force of the liquid on the front window of the aquarium.
c. Evaluate the forces for a-long, deep aquarium filled with water.
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