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Thursday, 9 May 2019

JET PROPULSION IN FLUID MECHANICS

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 plateforce exerted by a jet on stationary curved plateforce 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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