Theory Reports Examples
The impinging jet experiment is done to investigate the force produced on a target due to a water jet. The jet is trained on vanes of different three shapes, conical, hemispherical, and a flat vane. The force generated on the impact surface by the deflected jet is compared to the momentum change of the water jet. The water jet impact is studied under Reynolds laminar flow with the Reynolds’s number ranging from 200-500. The impinging jet studies are used in the design of hydro turbines. Water jets are tangentially directed at the vanes of water turbines thereby producing torque. Impinging jets are used commercially with Pelton turbines for power generation. This combination produces a high efficiency of over 95% and capacities of over 100MW.
An impinging jet is defined as high velocity stream of water ejected from a nozzle and impinged on a barrier with the aim of doing work. The water jet in the impinging water jet experiment acts on three vane shapes, conical vane, flat disk, and hemispherical cup. The targets counter the force of the water jet in one dimensional net force which results in an axial momentum jet fluid.
The object being acted upon by the force of the jet produces a reaction force which acts downwards. The force due to the weight is equal to the force due to the water jet just when the jet displaces the weight. The momentum of the water jet is transferred to the weight according to the law of conservation of momentum, pushing it upwards. In a fluid, steady conservation of translation momentum is given by
The sum of the forces acting on the vane,, is given by the fluid acting on it, the fluid weight of the, viscous drag, and the pressure acting on the control surface.
Fymeas = force acting on the vane
ρ = density of water
V = average jet velocity assuming uniform distribution
A = area at nozzle exit = 7.82 mm /4*3.14159= 47.78mm2.
μ = dynamic viscosity of water = is 8.90 × 10−4 Pa•s
v = kinematic viscosity of water.
θ’ = the angle of cones
d = diameter (given as 8mm)
Q = flow rate in liters / sec
The calculations for experimental force coefficient is given by
The nozzle’s Reynolds number which defines the jet’s laminar flow is given by:
The theoretical experimental values for force and mass flow rate is calculated as
The theoretical force coefficient is given by:
Hence, by substitution, the theoretica force exerted on the vane can be given as,
The last two equations gives the relation between actual and theoretical vales.
The three different shapes of vanes used means that water will hit the impact surface at different angles in respect to the vanes’ axis. Therefore, the same jet will result to forces of different magnitude in each vane. The resulting force per each vane shape is determined by the angle of impact of the impinging jet and is given by:
For a flat plate impact surface, :
Conical vane target,:
Hemispherical cup target, :
Apparatus and procedure
The apparatus used in the impinge jet experiment are a 7.8mm water nozzle, three impact vanes, a spring scale, flow meter, water plumbing and a stand to support the apparatus.
Figure 1 show the experiment set up. Water from the tank has enough head to force a jet out through the flow meter and the nozzle. The jet from the nozzle then impinges on the vanes mounted on the target plate. The weight on spring scale pan determines the force required to deflect the jet.
The vane is coupled to a lever which carries the weight. The lever is set at a balanced position with the weight at the zero position, which is shown by a tally supported by the lever. The force due to the water jet is measured by the moving of the weight, which is fully indicated by the movement of the tally back to its original balanced position.
Figure 1: Impinging jet experiment apparatus set up
The apparatus is leveled at a balanced position and water is admitted though the nozzle. The flow rate is steadily increased until the vane displaces the lever. The discharged water is used to determine the mass flow rate by collecting it over a given duration of time. The flow rate is adjusted to give several readings of the weight displacement.
For the flat plate impact surface, sample calculations taking m=0.2Kg, nozzle diameter is 7.8mm, m=0.2Kg, t=64.39, g = 9.81 m/s2, and ρ=1000 kg/m3
A=πr2= π(d2)2= π(7.8×10-32)2=4.78×10-5m2
but Fy= ρQ2A →Q=Fy*Aρ= 1.962*4.78×10-51000=3.06×10-4m2/secor L/sec
ReD= ρVDμ= 1000*6.40*4.78×10-58.90×10-4=343.8
Experimental force coefficient
CF= Fy0.5*ρAV2= 1.9620.5*1000*4.78×10-5*6.402=2.00
Fy= ρQ2A= 1000*(3.06×10-4)24.78×10-5= 1.96N
Theoretical force coefficient,
CF= Fy0.5*ρAV2= 0.9730.5*1000*4.78×10-5*6.402 =0.99
The above table shows deviation between empirical and theoretical results. Discrepancies between the results and the expected theoretical values can be attributed to inaccuracies equipment and dissimilar test conditions with those of the theoretical results
m=ρgA=2.132 e 6
The experimental mass can be obtained from the gradient of
mexperimental"graph”= y2-y1x2- x1=2.135 e6
%d= mexp-m(theo)m(exp)=0.04 %
%d= 2.135 e6-2.132 e 62.135 e6=0.14 %
Error in volume is dV= 0.5L
dQ= dV as (Q=V/t), dV = 0.5L= 5 e-3 m3 /t
Velocity error is dV=dQ= 5 e-3 m /s
Error in mass dm = 0.0005 kg
Error in weight dF = 0.0005 * 9.81 = 4.90e-3 N
The results presented in this paper have shown that an impinging jet exerts force on a surface, and that the force exerted on an object depends on its shape. The action of an impinging jet displaces weights placed vertically above it by applying a force equivalent to the reaction force due to the weight. This paper has examined and established that the force exerted on an impact surface by a jet is directly proportional to the rate of flow and the Reynolds number of the nozzle.
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