We have seen various topics such as force
exerted by a jet on vertical flat plate, force
exerted by a jet on stationary inclined flat plate, force
exerted by a jet on stationary curved plate, force
exerted by a jet on a hinged plate, force
exerted by a jet on a curved plate, force exerted by a jet of water on a series of vanes and force exerted by a jet of water on a series of radial curved vanes in
our recent posts.
Now we will see here the basics of jet propulsion
with the help of this post. Further, we will also find out here the following
points as mentioned here.
Jet Propulsion definition
Jet propulsion of a tank with an orifice
Condition for maximum efficiency
Equation for maximum efficiency
Let us start here our discussion with definition
part of jet propulsion.
Jet propulsion
Jet propulsion means the propulsion or movement of
the bodies such as ships, aircrafts, rocket etc., with the help of jet.
The reaction of the jet, coming out from the orifice
provided in the bodies, is used to move the bodies.
Confused????...... Okay, let me explain you.
Let us consider that a jet of fluid, coming out from
an orifice provided in the body, striking a plate. Jet of fluid will exert the
force on the plate, when fluid jet will strike the plate. The magnitude of this
force, exerted by the jet of fluid over the surface of plate, will be determined
on the basis of condition and shape of the plate.
Magnitude of this force will
be dependent over the factor e.g. whether plate is moving or stationary, whether
plate is curved, flat or inclined.
This force, exerted by the jet of fluid over the
surface of plate, will be termed as action of jet. Let us recall Newton’s third law i.e. every action
will have one equal and opposite reaction.
Therefore jet of fluid while coming out from an
orifice, provided in the body, will exert a force on the orifice or body in opposite
direction in which jet will be coming out. Magnitude of this force will be
equivalent to the action of jet. This force, acting on the orifice or body in
opposite direction, will be termed as reaction of jet.
If the body, in which orifice is fixed, is free to
move. Body will be started to move in the opposite direction of jet of fluid.
Jet propulsion of a tank with an orifice
Let us consider we have one large tank and one
orifice is fixed with the tank to its one side as displayed here in following
figure.
Let us consider the following terms from above
figure.
H = Constant head of water in tank from the orifice
center
a = Area of orifice
V = Velocity of jet of fluid
CV = Co-efficient of the velocity of
orifice
V = CV x Square root of (2 g H) = CV
x (2 g H) 1/2
u = Velocity of tank
Force exerted on the tank
Force exerted on the tank will be given by following
formula as displayed here.
Work done on the moving tank by jet of fluid
Work done on the moving tank by jet of fluid per
second will be given by following formula as mentioned here.
Efficiency of propulsion will be determined as mentioned here
Efficiency of propulsion = Work done per second /
Kinetic energy of the issuing jet per second
Condition and expression for maximum efficiency
For a given value of V, efficiency will be maximum
when dη/du = 0.
After differentiating the efficiency with respect to
the velocity of tank i.e. u, we will have one condition for maximum efficiency
i.e. V = u
Condition for maximum efficiency, V = u
After putting the value of V = u in the equation of
maximum efficiency, we will have one value of maximum efficiency and that is
50%.
Maximum efficiency = 50%
Do you have any suggestions? Please write in comment
box.
We will see another topic i.e. Jet propulsion of ships, in the subject of fluid mechanics, with the help of our next post.
Reference:
Fluid mechanics, By R. K. Bansal
Image courtesy: Google
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