Summary:

The purpose of the experiment was to develop a calibration curve for a rotameter so that it may be used to measure flow in a pipe. The rotameter is a very commonly used flow measuring device, especially in low pressure systems. It is used for both liquid and gas flows. It is a variable area meter which consists of a vertical, tapered, transparent tube containing a float. The float moves upward as the fluid flow increases. A variable ring or annulus is created between the outer diameter of the float and the inner wall of the tube. As the float moves upward in the tube, the area of the annulus increases. The float will continue to move upward until a pressure drop across the float, which is unique for each rotameter, is reached. This pressure drop across the float is constant regardless of the flow rate. The mass flow rate of water was measured by taking mass of water & corresponding time interval for different float level reading of rotameter. From the readings the rotameter coefficient (C) and Re/C were calculated and then plotted on the graph paper. This plot is independent of fluids an applicable for the specific rotameter. From the plot the rotameter coefficients for kerosene were determined. And then the flow rates were calculated to plot a rotameter reading vs. flow rate graph for the both fluids. The plot is found linear and the slope of the line of kerosene is greater than that of water.

Apparatus:

1. A rotameter

2. A bucket

3. A stop watch

4. Manometer

5. A pipe

6. Pump

7. Water reservoir

Experimental Setup:

Figure 1: Schematic Diagram for Calibration of Rotameter

Observed Data: Temperature of the water = 31.6C

Temperature of the room = 30C

Mass of empty bucket = 0.7 kg

Diameter of the rotameter tube at lower end, D1 = 1.5 inch

Diameter of the rotameter tube at upper end, D2 = 2.0 inch

Total length of rotameter tube, L = 100 divisions

Maximum float diameter, Df = 1.5 inch

Volume of the float, Vf = 1.077x10-3 ft3

Density of the float, Sf = 486.93 lbm/ft3

Table 1 : Observed data for rotameter and manometer reading

Number ofObservation

Weight ofWater + Bucket

(Kg)

Rotameter Reading

Time Interval(S)

ManometerReading

(inch)

Left Right

1 0.9 10 10.7 14 13.6

2 3.2 20 9.8 14.3 13.3

3 4.4 30 9.9 14.5 13.2

4 5.7 40 9.3 14.6 13.1

5 7.1 50 9.7 14.8 13

6 8.7 60 10.5 15 12.9

7 9.7 70 9.9 15.2 12.8

8 10.9 80 10.1 15.5 12.7

Calculated Data:

Density of water at 300C, ρw = 995.7 Kg/m3

Viscosity of water at 300C, µw =7.98x10-4 N.s/m2

Specific weight of water at 300C, γw= 9.764 KN/m3

Density of kerosene at 200C, ρk = 808Kg/m3

Viscosity of kerosene at 200C, k = 19.2x10-4N.s/m2

Density of mercury at 200C, ρm=13550 kg/m3

Table 2: Manometer Reading in SI Unit

Manometer Reading

(inch)

Difference in

Manometer Reading

(inch)

Difference in

Manometer Reading

(m)Left Column Right Column

14 13.6 0.4 0.01016

14.3 13.3 1.0 0.0254

14.5 13.2 1.3 0.03302

14.6 13.1 1.5 0.0381

14.8 13 1.8 0.04572

15 12.9 2.1 0.05334

15.2 12.8 2.4 0.06096

15.5 12.7 2.8 0.07112

Table 3: Calculation of Equivalent Diameter, Volumetric Flow rate

and Pressure Drop

Mass flow

rate of water

(Kg/s)

Volumetric flow

rateQw¿ 104

(m3/s)

Diameter of the

rotameter at the

level of float

Dt103

(m)

Equivalent

diameterDeq103

(m)

AnnulusArea

A0 105

(m2)

Difference in

Manometer

Reading

(m)

Velocity of the flow

(m/s)

Head Loss

ΔH

(m)

0.01869 0.1877 39.4 1.3 7.913 0.01016 0.2372

0.1828

0.2551 2.562 40.64 2.54 15.71 0.0254 1.631

0.3737 3.753 41.9 3.8 23.876 0.03302 1.572

0.5376 5.399 43.2 5.1 32.565 0.0381 1.658

0.65979 6.626 44.45 6.4 41.169 0.04572 1.609

0.7619 7.652 45.7 7.62 50.02 0.05334 1.5298

0.9091 9.13 46.9 8.89 58.748 0.06096 1.554

1.0099 11.04 48.3 10.16 69.216 0.07112 1.595

Table-4: Table showing Rotameter Coefficient for water and kerosene (from graph), Reynolds No, Rotameter coefficient,

volumetric flow rate of Kerosene

Reynolds

No.

Re

Rotameter coefficient for water,

Cw

(Re/C)w,

(for

Water)

(Re/C)K ,(for

Kerosene)

Rotameter Coefficient for

Kerosene (from graph),

CK

Flow rate of

Kerosene,QK104

(m3/sec)

384.71 0.1253 3071.87

5169.1 0.8611 6002.013 2278.1 0.91 3.047

7453.53 0.8301 8979.4 3408.2 0.88 4.478

10550.7 0.8755 12051.3 4754.1 0.87 6.038

12848.8 0.8496 15123.2 5740.04 0.86 7.545

14545.9 0.8078 18006.06 6834.24 0.859 9.157

17238.0 0.8206 21007.07 7973.3 0.85 10.64

20219.6 0.8422 24008.08 9112.32 0.848 12.508

Sample Calculation:

Sample Calculation for Rotameter reading 20 (2nd Observation):

Diameter of the rotameter tube at upper end, D2 = 2.0 inch

= 2.02.5410-2m

= 5.0810-2m

Maximum float diameter, Df = 1.5 inch

= 1.52.5410-2m

= 3.8110-2m

Density of the float,S f=486 .93

lbft 3

=486.93lbft 3

×0.4536Kglb

×(0 .3048mft )

3

=7800Kgm3

Area of the float, A f=

πDf 2

4=π×(3 .81×10−2 )2

4=1 .14×10−3m2

Volume of float, Vf = 1.07710-3ft3 = (1.07710-3ft3) (0.3048m/ft)3

= 3.0497210-5m3

Maximum diameter of rotameter tube at the cross-section of the float,

Dt= D f + (D2−D f )×R100

=3 . 81×10−2+ (5.08×10−2−3 .81×10−2 )×20100

=40 .64×10−3m

Equivalent diameter, Deq = (Dt - Df) = (4.06410-2- 3.8110-2 )m = 2.5410-3m

Annulus cross-sectional area

Ao=π4 (Dt2−Df 2)=

π4×[ ( 4 . 064×10−2 )2−( 3. 81×10−2)2]=1 . 571×10−4m2

Calculation of Rotameter co-efficient, ‘C’ &‘Re/C’ (for water)

Mass of water and bucket = 3.2 kg

Mass of empty bucket = 0.7 kg

Mass of water = (3.2 – 0.7) = 2.5 kg

Time of taking water = 9.8 sec.

So, Mass flow rate of water =mt

¿2.5kg9.8 sec

= 0.2551 kg/sec

So, Volumetric flow rate of water, Qw =mass flow rate of waterdensity of water

¿ 0.2551kg/ sec995.7kg /m 3

= 2.562 X 10-4 m3/sec

Pressure drop due to head loss of water,

ΔHW = VfAf×( ρf−ρw

ρw) = 3.0497210−5

1.14×10−3 ×(7800−995.7995.7

)

= 0.1828 m

Rotameter co-efficient for water,

Cw=Q

A0√2gΔH= 2 .562×10−4

1 .571×10−4×√2×9 .81×0 .1828=0. 8611

Now, as

ReC

=Deqρμ

√2 gΔH

(ReC )w=Deq

ρwμw

√2gΔHw

¿2.54×10−3×995 . 7

7 .98×10−4 √2×9 .81×0 .1828

¿6002.013

Velocity of fluid flow, v = Qw/A0

= (2.562x10-4/15.71x10-5) m/sec

= 1.631 m/sec

Difference Of manometer reading, R = (14.3 – 13.3) inch

= 1.0 inch

=0.0254 m

Experimentally,

ΔHw= R×(ρHg− ρwρw

)

= 0.0254 X (13550−995.7

995.7¿

= 0.3203 m

Rotameter Co-efficient for water,

Cw=Q

A0√2gΔH= 2 .562×10−4

1 .571×10−4×√2×9 .81×0 .3203=0 .6505

Calculation of Re

ℜ=(Deq×V × ρw)

µw = (2.54X10-3 X 1.631 X 995.7)/7.98X10-4

= 5169.1

Calculation of Rotameter co-efficient, ‘C’ &‘Re/C’ (for kerosene)

Pressure drop due to head loss of kerosene,

ΔHK = VfAf×( ρf−ρk

ρk) = 3.0497210−5

1.14×10−3 ×(7800−808808

)

= 0.2315 m

(ReC )k=D eq

ρkμk

√2 gΔHk

¿ 2. 54×10−3×808

19 .2×10−4 √2×9 . 81×0 . 2315

¿2278.1

The value of rotameter efficient for Kerosene has to calculate from the Graph-1.

The value of Rotameter coefficient for Kerosene (Ck) is 0.91 when Re/C = 2278.1.

Calculation of volumetric flow rate for kerosene (Qk):

CkCw

=Qk√ΔH k

Qw√ΔHw

⇒Q k=QwCk√ΔHk

Cw√ΔHw

=2 .562×10−4×0 . 91×√0 .23150. 8611×√0 .1828

= 3.047×10-4 m3/s

Graphs:

5000 10000 15000 20000 250000.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

Graprh 1: (Re/C)w vs Cw

Cw

(Re/C)w

CW

10 20 30 40 50 60 70 80 900

2

4

6

8

10

12

14

Graph 2: Rotameter reading vs Volumetric Flow Rate

Flow Rate of WaterLinear (Flow Rate of Water)

Rotameter Reading (R)

Vol

umet

ric

Flow

rate

(Q x

104)

(m3/

s)

Results: The results of this experiment have been tabulated below with a comparison between

water and kerosene:

Table-4: Experimental pressure drop, Rotameter coefficients and the volumetric flow rates

for both water and kerosene.

Observati

on

number.

For Water For Kerosene

Pressure

Drop

ΔH

(m)

Rotameter

Co-

efficient

(Cw)

Volumetric

flow rate

Q×104

(m3/s)

Rotameter

Coefficient

(from graph),

(CK)

Volumetric

Flow rate

QK104

(m3/sec)

1 0.1253 0.1877 0.01016

2 0.8611 2.562 0.91 3.047 0.0254

3 0.8301 3.753 0.88 4.478 0.03302

4 0.8755 5.399 0.87 6.038 0.0381

5 0.8496 6.626 0.86 7.545 0.04572

6 0.8078 7.652 0.859 9.157 0.05334

7 0.8206 9.13 0.85 10.64 0.06096

8 0.8422 11.04 0.848 12.508 0.07112

Discussion:

From theory we know that volumetric flow rate and Rotameter reading are proportional to each other. When the curve for Volumetric flow rates, Q vs. Rotameter readings, R was drawn for water and kerosene (Graph 2), both of the curves were linear, but the straight line for kerosene was above the straight line for water, because the density of kerosene is less than the water and the volumetric flow rate of kerosene for the same Rotameter reading was larger than the flow rate of water.

The value of Rotameter coefficient C and the Re/C for water flow were plotted in a graph paper (Graph 1). This curve has been found downward with negative slope. Theoretically the curve is unique for a Rotameter for all the fluids. So the term C was also calculated for kerosene from this curve using the value of Re/C.

In this experiment, the data observed gave quite accurate results, but some errors were introduced in the results due to the following reasons:

The manometer tube was between the two ends of rotameter in the pipe system. Hence there might be a friction loss occur in the rotameter which was not counted in our calculation. So discrepancies were found between theoretical head and experimental head.

The head losses for water and kerosene are theoretically constant values and were found to be 0.1828m and 0.2315m. But practically the manometer readings were not found a constant. This loss was occurred because of the friction of water with the pipe surface, which was not smooth enough.

Rotameter reading depends on gravitational force. So it is necessary to maintain the vertical position of Rotameter. Due to the turbulent flow of water the vertical position was distorted.

The mass of the water collected in a bucket had been measured manually by a simple weight machine. There might be some mistakes while we took the weight and as a result it was not possible to get the accurate mass flow rate for each steady flow.

The apparatus that we used here mainly the pipe line is now in damaged condition as these lines are used for so many times before. So the surface may be in rough

condition so the variation in the results came. It also contributed to the error in calculating the Diameter of the pipe from standard references. This might be an important reason for the discrepancy in our theoretical and experimental head losses.

The manometer readings taken may have been subjected to parallax error.

The flow property could have changed due to the temperature change of water. Though the initial temperature of the water was recorded, the final temperature was not determined and as the result the temperature variation of different variables remained unconsidered in the calculation.

All the data were taken for short time period. Before reaching the steady state another data was taken. This may caused some discrepancies.