We
are dealing with the series of problems based on fluid statics and fluid
dynamics. When a fluid is in the state of motion, it has potential
energy,kinetic energy and also pressure energy. We know that the total energy
of the system is constant. As per Bernoulli's theorem, the sum of potential
energy,kinetic energy and pressure energy per unit mass always remains
constant. We can also consider the viscous force acting opposite to the motion.
It is the force that always opposes the relative motion. It depends on the area
of cross section of the fluid, velocity of the fluid flow and the distance
between the two layers of the fluid in the motion.
Problem
A
vessel is kept on a table and filled with water. From the bottom of the vessel,
a orifice is made and its location is given in the problem as shown in the
diagram below. We need to measure the horizontal distance at which it is going
to strike the floor.
Solution
We
know that the velocity of the fluid coming out of orifice is similar to a
velocity of a freely falling body and it depends on the height of the fluid
above the opening. Once it is out, it is under the influence of the gravity and
its horizontal distance distance can be measured with the equations of
motion.There is no gravity acting on it so its velocity is uniform along
horizontal direction. Further problem can be solved as shown in the diagram
below.
Problem
Velocity
of air flow on the upper surface of the wing of airplane is 40 meter per second
and on the lower surface is 30 meter per second and its area of cross section
is given to us and its mass is also given to us. We need to measure the force
experienced by the wing and the problem is as shown in the diagram below.
Solution
As
the wing is airplane is horizontal, there is no change in potential energy and
we can remove that components of Bernoulli's theorem. Applying kinetic energy
data, we can get the difference in the pressure at both the cases. We know that
pressure is the force per unit area and hence we can measure the force acting
on the system as shown in the diagram below.
Problem
Specific
gravity of two liquids combined together when they have same mass and volume is
given to us and we need to measure the density of each liquid. The problem is
as shown in the diagram below.
Solution
We
know that the density is the ratio of mass to the volume. We can find the
effective density of the system when they have equal volume and equal mass can
be found as shown in the diagram below. We have all ready derived equations for
both of them and it can be done as shown below.
Problem
A
sphere has known density and it is falling through a fluid of known density and
we need to measure the acceleration of the body and the problem is as shown in
the diagram below.
Solution
When
a body is moving in a fluid, its weight acts in the downward direction and the
upthrust acts in the upward direction. We need not consider viscous force as
there is no data about coefficient of viscosity. We can write equation for the
resultant force as the difference between weight and upthrust. We can use
Newton’s second law and find as shown in the diagram below.
Problem
When
a polar bear jumps on to ice block it just sinks and we need to measure the
weights of that ice block and the specific gravity of ice and sea water is
given to us. Problem is as shown in the diagram below.
Solution
We
know that weight of the liquid displaced is the sum of weights of ice block and
polar bear. We can equate the data and solve the problem as shown in the
diagram below.
Related Posts
Problems on Bernoulli's theorem and Its Applications
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