Equipement Collecting tank, transparent cylinder, nozzle of 10 mm dia. Flat vane, curved hemispherical vane and pressure gauge.
Introduction and theory:Momentum equation is based on Newton’s second law of motion which states that the algebraic sum of external forces applied to control volume of fluid in any direction is equal to the rate of change of momentum in that direction. The external forces include the components of the weight of the fluid and of the forces exerted externally upon the boundary surface of the control volume.
If a vertical water jet moving with velocity v is made to strike a targety, which is free to move in the vertical direction, then a force will be exerted on the target by the3 impact of jet. According to momentum equation this force ( which is also equal to the force required to bring back the target in its original position) must be equal to the rate of change of momentum of the jet flow in that direction.
Applying momentum equation in x direction
-Fx= ρQ[νx.out- νx.in]
= ρQ[ν.cosβ- ν]
Fx= ρQν[1-cosβ]
For flat plate,β = 900/p>
Fx= ρQ ν
For hemispherical cup, β = 1800
Fx= 2ρQ ν
Here ρ is the mass density, Q the discharge through the nozzle, v the velocity at the exit of the nozzle (i.e., Q/a) and a is the area of cross section of the nozzle.
Therefore Fx= ρQ2/a
While for curved hemispherical vane the force is Fx= 2ρQ2/a
Experimental set up:The experimental set up primarily consists of a nozzle through which a water jet imerges vertically in such a way that it may be conveniently observed through the transparent cylinder. It strikes the target vane positioned above it. The force applied on the vane by jet can be measured by applying weight to counteract the reaction of the jet. Vanes are interchangeable i.e. flat, inclined or curved vane.
Arrangement is made for the movement of the plate under the action of the jet and also because of the wt. Placed on the loading pan. A scale is provided for carrying the vanes to its original position i.e. as before the jet strikes the vane. A collecting tank is used to find the actual discharge and velocity through the nozzle.
Experimental procedure:
Note down the relevant dimension as area of collecting tank, mass density of water and dia. Of nozzle.
The flat plate is installed
When jet is not running, note down the position of upper disc.
The water supply is admitted to the nozzle and the flow rate adjusted to its max. value.
As the jet strieks the vane, position of upper disc is changed. Now place the wts. To bring back the upper disc to its original position.
At this position find out the discharge as well as note down the wts. Placed on the upper disc.
The procedure is repeated for each value of flow rate by reducing the water supply in steps.
The procedure is repeated with the installation of inclined or curved vane in the apparatus.
Curved Hemispherical Vane
When jet is not running, position of upper disc =
------------------------------------------------------------------------------------------------------------Run Discharge measurement Balancing Theoretical Error in %
No
Initial (cm)
Final (cm)
Time(sec)
Discharge(cm3/sec)
Mass W
Force F
Force F' = 2ρQ 2/a dyne
F-F'/F'
Comment:The main source of error in the experiment is in assessing the exit velocity component. Also hemispherical cup require more force to balance than the flat plate.
Precautions:
Apparatus should be in leveled condition.
Reading must be taken in steady or near by steady conditions by watching the pressure gauge.
Discharge must be varied very gradually from a higher to smaller value.
Observation and computation sheet:
Dia of nozzle = 10mm
Mass density of water ρ =
Area of collecting tank =
Area of nozzle a=
Horizontal flat plate
When jet is not running, position of upper disc is at =
Run Discharge measurement Balancing Theoretical Eoor in %
No Initial(cm) Final(cm) Time(cm) Discharge cm3/sec Mass W(gm) Force F(dyne) Force F'= ρQ2/a(dyne)/F-F'/F'
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