Lab 1 – Impact of Jet

Course: CE 3142-001 – Fluids Laboratory

Date Performed: June 8, 2011

Group Members: Michael York, Jose Rojas, Sandip Tamrakar, Jarryd Tibbetts (Group 4)

Submitted By: Michael C. York

Date Due: June 15, 2011

Date Submitted: June 15, 2011

Professors: Amir Norouzi

Abstract

The objective of this experiment is to study the force of a jet as it impacts targets with varying deflection angles. To do this, a jet stream will be applied to targets of various deflection angles, and weights will be applied to balance the force of the impact from the jet stream. The quantity of weight will be recorded, and through calculations, a relationship between the theoretical calculated force and the experimental measured force can be obtained and analyzed.

Introduction

The purpose of this experiment is to determine the reaction force produced by the impact of jet of water on to targets with different deflection angles. Also, to experimentally determine the force required to keep a target at an equilibrium level while it is subjected to the impact of water jet. The final purpose of this experiment is to compare the experimentally measured force with the theoretical calculated force.

When a jet of water flowing with a steady velocity strikes a solid surface, the water is deflected to flow along the surface. Newton’s second law of motion states that “the change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.” The analogy to Newton’s second law in fluid mechanics is known as the momentum equation.

For all diagrams, equations, and derivations necessary to explain, identify, and clarify the work and conditions investigated, reference the “Impact of Jet” handout in the appendix.

Procedure

For description of apparatus, procedures, application to theory, routine maintenance procedures, and a related diagram reference the “Impact of Jet” handout in the appendix.

Raw Data Table

RAW DATA TABLE

Sr. no. Nozzle Diameter

Deflector Type(α)

Volume Collected

(V)

Time to Collect

(t)

Mass Applied

(m)

Area(A)

Density*(ρ)

(m) (degrees) (L) (s) (kg) (m2) (kg/m3)1 0.008 90 4 22.6 0.110 5.0265E-05 10002 0.008 90 4 18.6 0.300 5.0265E-05 10003 0.008 90 4 8.9 0.300 5.0265E-05 10004 0.008 90 4 12.2 0.230 5.0265E-05 10005 0.008 120 4 17.6 0.140 5.0265E-05 1000

6 0.008 120 4 13.3 0.225 5.0265E-05 10007 0.008 120 4 9.7 0.375 5.0265E-05 10008 0.008 120 4 10.0 0.370 5.0265E-05 10009 0.008 180 4 17.2 0.180 5.0265E-05 1000

10 0.008 180 4 13.2 0.295 5.0265E-05 100011 0.008 180 4 11.9 0.405 5.0265E-05 100012 0.008 180 4 36.3 0.060 5.0265E-05 1000

*Density of water was assumed to be 1000 kg/m3

Sample Computations

Calculations & Formulas

Sr. no. Nozzle Diameter

Deflector Type(α)

Volume Collected

(V)

Time to Collect

(t)

Mass Applied

(m)

Weight Applied

(W)

Flow Rate(Qt)

(m)(degrees

) (L) (s) (kg) (N) (m3/s)1 - 4

given90

chosen recorded determined mG(G = 9.81 m/s2)

Vt/t5 - 8 1209 - 12 180

% Error formula used: (Calculated Slope – Measured Slope) / Measured Slope

Calculations & Formulas (cont.)

Volume Collecte

d(Vt)

Area(A)

Velocity(v)

Velocity2(v2)

Force(Fy)

Theoretical Slope(s)

Density(ρ)

(m3) (m2) (m/s) (m/s)2 (N) (kg/m) (kg/m3)

V/1000 given Qt/A v2 ρAv2(cos(180- α)+1) ρA(cos(180-α)+1) determined

Results

As it is apparent from the results of this experiment, the velocity and the reaction forces are proportional in their amounts. The theoretical calculated slope was larger compared to the experimental measured slope for the 120 degree target, but smaller than the 90 and 180 degree targets.

The theoretical calculated slope shows that the 120 degree, hemispherical, target has the lowest flow rate. However, the experimental measured slope shows that the 90 degree target has the

lowest flow rate. The results display inconsistencies which indicate errors incurred during the procedure. It is also apparent that the errors were largest for the 90 degree target.

0.0010.00

20.0030.00

40.0050.00

60.0070.00

80.0090.00

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

f(x) = 0.00839383018478424 x + 0.00988658437186138f(x) = 0.00512153770057714 x + 0.0382272853220325

f(x) = 0.00163775533108199 x + 0.172274600868367

Velocity2 vs. mass

90 Degree TargetLinear (90 Degree Target)120 Degree TargetLinear (120 Degree Target)180 Degree TargetLinear (180 Degree Target)

Velocity2 (m/s)2

mass(kg)

RESULTS TABLE

Sr. no. Nozzle Diameter

Deflector Type(α)

Volume Collected

(V)

Time to Collect

(t)

Mass Applied

(m)

Weight Applied

(W)

Flow Rate(Qt)

(m) (degrees) (L) (s) (kg) (N) (m3/s)1 0.008 90 4 22.6 0.110 1.079 1.77E-042 0.008 90 4 18.6 0.300 2.943 2.15E-043 0.008 90 4 8.9 0.300 2.943 4.49E-044 0.008 90 4 12.2 0.230 2.256 3.28E-045 0.008 120 4 17.6 0.140 1.373 2.27E-046 0.008 120 4 13.3 0.225 2.207 3.01E-047 0.008 120 4 9.7 0.375 3.679 4.12E-048 0.008 120 4 10.0 0.370 3.630 4.00E-049 0.008 180 4 17.2 0.180 1.766 2.33E-04

10 0.008 180 4 13.2 0.295 2.894 3.03E-0411 0.008 180 4 11.9 0.405 3.973 3.36E-0412 0.008 180 4 36.3 0.060 0.589 1.10E-04

RESULTS TABLE (cont.)

Volume Collecte

d(Vt)

Area(A)

Velocity(v)

Velocity2(v2)

Force(Fy)

Theoretical Slope

(s)

Density(ρ)

Error

(m3) (m2) (m/s) (m/s)2 (N) (kg/m) (kg/m3) (%)

0.004 5.0265E-05 3.52 12.40 0.3440 0.02774258 1000 16.33911

0.004 5.0265E-05 4.28 18.30 0.5078 0.02774258 1000 16.33911

0.004 5.0265E-05 8.94 79.95 2.2180 0.02774258 1000 16.33911

0.004 5.0265E-05 6.52 42.55 1.1804 0.02774258 1000 16.33911

0.004 5.0265E-05 4.52 20.44 0.0489 0.002391962 1000 0.530988

0.004 5.0265E-05 5.98 35.80 0.0856 0.002391962 1000 0.530988

0.004 5.0265E-05 8.20 67.30 0.1610 0.002391962 1000 0.530988

0.004 5.0265E-05 7.96 63.33 0.1515 0.002391962 1000 0.530988

0.004 5.0265E-05 4.63 21.41 2.1519 0.10053 1000 10.96786

0.004 5.0265E-05 6.03 36.34 3.6537 0.10053 1000 10.96786

0.004 5.0265E-05 6.69 44.72 4.4956 0.10053 1000 10.96786

0.004 5.0265E-05 2.19 4.81 0.4831 0.10053 1000 10.96786

Application & Significance

From this experiment, it can be concluded that the impact of a jet will be greatest upon a target with a deflection angle of 180 degrees. This could be important for industries that are involved in work pertaining to jet propulsion, as well as other industries that work with jet streams of similar nature.

Discussion, Conclusion, & Recommendations

In conclusion, the calculated theoretical force is correlated with the experimental measured force. Both forces have a directly proportional relation. Theoretically, both forces should be equal, however this is not the case due to errors incurred during the experiment. It can be determined from this experiment that higher water jet velocity will produce a higher force exerted onto the

target vane. The amount of weight required to achieve a state of equilibrium is directly proportional to the amount of force exerted by the jet.

According to the results, the theoretical calculated slope shows that the 120 degree, hemispherical, target has the lowest flow rate. However, the experimental measured slope shows that the 90 degree target has the lowest flow rate. These inconsistencies infer that errors were accumulated during the procedure. Most likely, the errors occurred during the recording of the time taken to collect the desired volume.

I believe that this experiment could possibly be improved by choosing a higher collection volume. I believe that this would allow for less error when recording the time to collect that volume because it would lengthen the time.

References

P.Kundu, and I.Cohen “Fluid Mechanics.” Academic Press. 2nd edition.

White, Mark M. “Fluid Mechanics.” Mcgraw-Hill College. 4th edition.

Appendix