FLUID MECHANICS

IMPULSE MOMENTUM PRINCIPLE TEST

RESULTS AND DISCUSSION

Flat Plate
Nozzle diameter	0.008	m
Area of nozzle	5.0265 x10-5	m2
Density of water	998	kg/m3

Deflector angle “a (degrees)	Mass Applied on spring “W”	Volume of water		Time to Collect Water “t”	Flow Rate “Q”	Experimental force (Direct Force)	Theoretical Force (Indirect Force)
degrees	kg	L	M3	s	m3/s	N	N
0	0	0	0	0	0.0000
0	0.1	15	0.015	66.08	0.0002	0.981	1.0231
0	0.2	15	0.015	46.09	0.0003	1.962	2.1030
0	0.3	15	0.015	38.6	0.0004	2.943	2.9983
0	0.4	15	0.015	33.75	0.0004	3.924	3.9219
0	0.5	20	0.02	40.47	0.0005	4.905	4.8491
0	0.6	20	0.02	36.53	0.0005	5.886	5.9515
0	0.7	20	0.02	33.75	0.0006	6.867	6.9723
0	0.8	25	0.025	39.62	0.0006	7.848	7.9053
0	0.85	25	0.025	37.52	0.0007	8.3385	8.8149
				Average	0.0005	4.8505	4.9488

Table 1 Data collected in laboratory and calculated forces for the Flat Plate

Fig.1 Plot Direct and Indirect Force for the flat plate

Fig.2 Plot Direct Force vs volume flow rate” Q” for the flat plate

HEMISPHERICAL CUP
Nozzle diameter	0.008	m
Area of nozzle	5.0265 x10-5	m2
Density of water	998	kg/m3

Deflector angle “a (degrees)	Mass Applied on spring “W”	Volume of water		Time to Collect Water “t”	Flow Rate “Q”	Experimental force (Direct Force)	Theoretical Force (Indirect Force)
degrees	kg	L	M3	s	m3/s	N	N
0	0	0	0	0	0.0000
0	0.1	15	0.015	66.08	0.0002	0.981	2.0461
0	0.2	15	0.015	46.09	0.0003	1.962	4.2059
0	0.3	15	0.015	38.6	0.0004	2.943	5.9966
0	0.4	15	0.015	33.75	0.0004	3.924	7.8439
0	0.5	20	0.02	40.47	0.0005	4.905	9.6981
0	0.6	20	0.02	36.53	0.0005	5.886	11.9030
0	0.7	20	0.02	33.75	0.0006	6.867	13.9446
0	0.8	25	0.025	39.62	0.0006	7.848	15.8105
0	0.85	25	0.025	37.52	0.0007	8.3385	17.6299
				Average	0.0005	4.8505	9.8976

Table 2 Data collected in laboratory and calculated forces for the Hemispherical Plate

Fig.3 Plot Direct and Indirect Force for the hemispherical plate

Fig.4 Plot Direct Force vs volume flow rate”Q” for the hemispherical plate

Table 3 Upper and lower 95% confidence data for the flat plate

Table 4 Upper and lower 95% confidence data for the hemispherical plate

Fig.5 Plot Direct Force vs volume flow rate” Q” for the flat plate

Fig.6 Plot Direct Force vs volume flow rate” Q” for the hemispherical plate

Table 5 Calculating direct force with the curve for the both flat and hemispherical plate

For flat plate, the maximum and a minimum indirect force for flat plate was 8.8149 N and 1.0231 N respectively. While the maximum and minimum direct forces were 0.981 N and 8.3385 N respectively. For the hemispherical plate, the maximum and minimum indirect force for the flat plate was 17.629 N and 2.0461 N respectively. While the maximum and minimum direct forces were 8.3385 N and 0.981 N respectively.
The linear equation obtained F_direct = 0.948 F _indirect+ 0.109. The squared value of R is 0.997. The value of slope (b) is 0.948

The differences between the values of the slope “b” obtained from the regression and the theoretical value of 1.0 is 0.052.

The differences between the exponents “n=0.989” obtained from the power regression fit and the theoretical value of 2.0 is 1.011.

The overall average for the ratio from the table 6 is 2.270652416. Compared to average value are 2.0. The Difference is 0.2706.

The potential sources of error are:-
Systematic error: – in this, calibration of the instrument may not be done properly.
Human Error: – While taking reading, if we add or remove masses, this is always associated.

Assumptions:

It is based on Newton’s second law; a so first assumption was there has to be unbalanced force.
Fluid is incompressible and steady.