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Example Questions
Example Question #101 : Fluids
A tank is completely full of water to the height of . On the side of the tank, at the very bottom a small hole is punctured. With what velocity does water flow though the hole at the bottom of the water tank?
The equation for determining the velocity of fluid through a hole is as follows:
This equation is actually derived from Bernoulli's principle. The is for velocity, the
is the acceleration due to gravity and
is the height. We solve for velocity by substituting for the values:
Example Question #32 : Fluid Dynamics
A syringe has a cross-sectional area of and the needle attached to the syringe has a cross-sectional area of
. The fluid in the syringe is pushed with a speed of
, with what velocity does the fluid exit the needle opening?
The correct answer is because the cross-sectional area of the syringe is
times larger than the needle opening. Therefore, the velocity will be
larger as well.
Example Question #33 : Fluid Dynamics
Pipe has radius
, and pipe
has radius
. The two pipes are connected. In order for the speed of water in pipe
to be
times as great as the speed in pipe
, what must be
?
The continuity equation says that the cross sectional area of the pipe multiplied by velocity must be constant. Let be the water speed in pipe
.
Example Question #101 : Fluids
A fluid is forced through a pipe of changing cross sections as shown. In which section would the velocity of the fluid be a maximum?
IV
II
III
I
All sections have the same velocity
II
Flow rate is equal to the product of cross-sectional area and velocity and must remain constant. Therefore, as the cross-sectional area decreases, the velocity increases.
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