Reynolds apparatus for demonstration for laminar and turbulent flows

1

33

1. Determination of velocity using PITOT TUBE apparatus

AIM

To determine the velocity of air using Pitot tube apparatus and draw the velocity profile.

APPARATUS

Pitot tube, blower, U tube manometer, Blower

THEORY

Pitot tube is a simple device used for measuring the velocity of flow. The basic principle used in this device is that at the stagnation point the kinetic energy is converted into pressure energy.CALCULATIONS

Velocity

Where Substituting the values of =1000 kg/m3 =1.16 kg/m3

m/sSPECIFICATIONSProcedure1. Mount the Pitot tube stand to a traversing mechanism on a suitable location and adjust the Pitot tube such that the total traverse covers the entire length of the flow region understudy.

2. Connect the two pressure taps of the Pitot tube to the manometer limbs.

3. Rotate the Pitot tube such that the difference in manometer liquid level is maximum. Now the Pitot tube is aligned to the flow. Note the angle and difference in the level of manometer liquid.

To measure the velocity at another point, traverse the Pitot tube (up and down) and then rotate the Pitot tube such that the difference in manometer liquid level is maximum. This is the flow direction in the new position. By noting the difference in angular position, the flow direction is determined with reference to a new point.

OBSERVATIONS AND CALCULATIONSSl no.

Probe position in x cms

Probe position in y cms

Pitot tube pressure(m of water)

Difference

h meters of water

Velocity

V m/s

h1

h2

SAMPLE CALCULATION(SET NO)h1 and h2 are the height of manometric fluid with h1>h2.the pressure difference h=h1-h2 m of water.

Density of water=1000 kg/m3Density of air=P/RT kg/m3Velocity=

PRESSURE DIFFERENCE H=(h1-h2)( ) m of water

RESULT

INFERENCE

2. VERIFICATION OF BERNOULLIS THEOREM

AIM

To verify Bernoullis theorem for liquid.APPARATUSa. Apparatus for the verification of Bernoullis theorem

b. Collecting tank

c. Stop watch

PRINCIPLE

Bernoullis theorem states that for a streamlined, steady, friction less and incompressible fluid flow, the sum of pressure head, velocity head and potential head (elevation) is a constant.

i.e. Pressure head (p/) + velocity head (v2/2g) + elevation (z) = Constant

Where, p = the pressure, N/m2.

y= the specific weight, N/m3.

v = Linear velocity of flow m/s.

g = Acceleration due to gravity, 9.81 m/s2.

z = Elevation from datum line, m.

Water at a constant head from a tank is allowed to flow through a horizontal pipe line of varying cross section. The pressure heads Hp1 HP2 etc. are noted from piezometers (say five) fitted at cross sections A1 A2, etc. By measuring the actual discharge, the actual velocities of flow at A1 A2, etc. are calculated.

The actual discharge, Qa = aR/t (m3/s).

Where,

a = area of measuring tank in m2.

R = rise of water in the measuring tank in m.

t = time in seconds to collect water for a rise of R metres in the measuring tank.The velocity of flow at the cross section A1 is given by

V1 = Qa/ A1 (m/s)

The velocity head, Hv1 = V12 / 2g (m of water)

Assuming that the pipe line has negligible frictional loss in flow, Bernoullis equation for the horizontal pipe at cross section A1 can be can be verified as:

Pressure head Hp1 + velocity head Hv1 = constant (in let head H)

OBSERVATIONS

Constants

1. Measuring tank size, a m2.

2. The rise (R m) for which the time t is noted to collect water in the measuring tank.

3. The areas of cross section A1 A2, etc. of the pipe

Variables

1) The piezometer readings Hp1 Hp2 etc. in m of water.

2) Time t seconds required to collect water for a height of R m in the measuring tank

TABULATION

Sl. NoH(m)t(s)P1P2P3P4P5P6Qa

(m3/s)

1

2

3

Sl NoV12/2gV22/2gV32/2gV42/2gV52/2gV62/2g

1

2

3

Sl NoP1 + V12/2gP2+ V22/2gP3 +V32/2gP4+V42/2gP5+V52/2gP6+V62/2gAvg.

Head(Havg)HeadLoss H- Havg

1

2

3

PROCEDURE

1. Open the inlet valve to the supply tank and allow water to fill up to a maximum head of H m.

2. Open the outlet valve of the apparatus to have flow through the testing pipe. Then regulate both the inlet and outlet valves so that the head H is maintained constant. This condition is reached only if the inlet is equal to outlet.

3. Note the time in seconds to collect water for a rise of h m in the measuring tank as t

4. Note the pressure head Hp at the areas of cross sections A1, A2, etc.

5. Repeat the experiment for medium and low heads in the supply tank.

CALCULATION

The cross sectional area of piezometer tape and their relative distance from the inlet in the converging and diverging dust is as follows

SectionDimension

Area

RESULT

Head loss is found to be very small and the average head loss is found to be ________

Hence the Bernoullis theorem is verified

INFERENCE

3. METCENTRIC HEIGHT AND RADIUS OF GYRATION OF FLOATING BODIES

AIM

To determine the metacentric height and radius of gyration of the given floating body

APPARATUS

a) Float tank with about 3/4th full of water,

b) Float with arrangement to measure the tilt due to displacement of a small weight

c) Stop watch.

PRINCIPLE

The float is tilted for an angle of from its horizontal position by placing a small extra weight w on one side of the deck of the float at a distance of x cm from the centre of the deck. The metacentric height, GM (the distance between centre of gravity and the metacentre) is calculated as

cm

Where,

w= the small extra weight in gms added on the deck.

W = the weight of the float in gm.

X = the distance of weight w from the centre, measured along the deck, in cm.

= the average of angle of tilt (L + R)/2 measured in degrees.

L and R are the angles of tilt measured, when the weight w is placed on duck at distance of x cm from centre to the left and right sides respectively. The radius of gyration of the float is calculated by noting the time for one free oscillation of the float.

Radius of gyration cm

Where,

tm = The mean time for one 'Oscillation in seconds.

GM = Metacentric height in cm.

PROCEDURE

1. Place the float in the float tank having water for about 3/4 height. Bring the float into horizontal position by screwing the tilt-adjusting nuts inward or outward, so that the plumb line passes through the zero mark of the tilt measuring device.

2. Place a small weight w, on one side (say left) of the float deck at a distance of x1 (cm) from the centre of the deck. Note the L shown by the plumb line.

3. Move the weight w, to the other side (right) of the deck for a distance of x1 cm from the centre and note the tilt shown by the plumb line as R

4. Repeat the steps 2 and 3 for four more distances and one more small weight w2,

5. Remove the weight and allow the float to oscillate. Note the time t (s) taken f 10 cycles of oscillations.

OBSERVATIONS

Constants

1) Weight of the float, W gm.

Variables

1) Extra small weights w1, and w2 in gm.

2) Distances of small weights from centre of deck x1 x2 and x3 cm measured towards the left and right sides.

3) Angle of tilt L and R in degrees.

4) Time noted, for 10 oscillations of float as t in seconds

TABULATION

For w1 = 250 gm

Sl Nox(cm)LRmGM(cm)K(cm)t(sec)

For w2 = 500 gm

Sl Nox(cm)LRmGM(cm)K(cm)t(sec)

SAMPLE CALCULATION

RESULT

The mean value of metacentric height

For 250 gm =

For 500 gm =

The mean value of radius of gyration

For 250 gm =

For 500 gm =

INFERENCE4.REYNOLDS APPARATUS FOR DEMONSTRATION FOR LAMINAR AND TURBULENT FLOWS

AIM:

To determine the nature of flow through a transparent pipe using Reynolds apparatus.

APPARATUS:

Reynolds apparatus, stopwatch

PRINCIPLE:

Reynolds no, Re=VD/;

Where, V=Average velocity of flow through the tube,

D= Diameter of the tube,

= density of the fluid,(1000 kg/m3)

=Dynamic viscosity of the fluid.

= kinematic viscosity For small flows, the dye stream moves as a straight line through the tube, showing that the flow is laminar. As flow increases, the Reynoldss number increases, since , and D are constant and V is directly proportional to the rate of flow. With increasing discharge, a condition will be reached at which the dye stream wavers and then suddenly breaks up and then diffuses or disperses throughout the tube. This shows that the flow has changed to turbulent flow.

For flow through tubes,

For Re Cc > Cd

Specification

Area of the orifice, a = --------m2 Area of tank, A = -------- m2

Procedure

1. Open the supply valve and fill the water in the orifice tank. Allow water to flow through the orifice and note the maximum head. 2. Divide the head approximately 7 steps for 7 sets of reading and adjust the inlet valve for steady flow and obtain a steady head H in the measuring tank twice as t1 & t2.if difference exceeds 10% take third reading which comes within the range3. Bring the hook gauge at the Vena Contracta and note x and y. Then move the gauge to another point on the center of the jet, at the farthest possible and note X1 and Y1 readings4. Close the drain gate valve of the collecting tank and note the time for say, 5cm rise in the tank5. Repeat the experiments for various head and tabulate observations.

Tabulation

X0 , Co-ordinate at the VenaContracta in X direction = -------m

Y0, Co-ordinate at the VenaContracta in Y direction = -------m

Sl.Nohead of

Water H cmX1

cmY1

cmX1-X0Y1- Y0Time for h in cm rise of water in t sec Actual discharge

Qa m3/secTheoritical dischargeQt

m3/s CvCc

Sample Calculation

Hook gauge headings at Vena Contracta X0 = --------- m

Y0 = ---------- m

Horizontal distance X for Vena Contracta = X1 - X0 = -------m

Vertical distance Y for Vena Contracta = Y1 - Y0 = ---------m

Time for h cm rise of water = ---------sec

Qa (Actual discharge)= (Area of tank x h) / time =(A x h)/t m3/sec

Qt (theoretical discharge) =a x (2gh) 1/2

Coefficient of discharge, Cd = Qa / Qt

Coefficient of velocity, Cv = X /(4YH)1/2

Coefficient of contraction, Cc = Area of jet at Vena contracta /Area of Orifice

Graphs:- Cd Vs H , Cv Vs H , Cc Vs H

Result

The values of hydraulic coefficients Cd = --------

Cv = --------

Cc = --------

Inference

10.DETERMINATION OF HYDRAULIC COEFFICIENTS OF mouth piece Aim

To determine the hydraulic coefficients, coefficient of discharge (Cd), and to draw the graph Cd vs. HApparatusWater tank fitted with mouth piece experimental setup, Piezometer fitted on the tank to measure the head over the mouth piece, Measuring tank, Meter scale, Stop watch.

Principle

Actual discharge, Qact = A h / t cm3/s

Where, A = Area of collecting tank

T = time taken for h cm rise of water in collecting tank

Theoretical discharge, Qt = a (2gH cm3/s

Where a = area of mouth piece in cm2

H = Head over mouth piece in cm

Therefore Cd = Qact / QtSpecification

Area of the mouth piece, a = --------m2 Area of tank, A = -------- m2

Procedure

1. Open the supply valve and fill the water in the mouth piece tank. Allow water to flow through the mouth piece and note the maximum head.

2. Divide the head approximately 7 steps for 7 sets of reading and adjust the inlet valve for steady flow and obtain a steady head H in the measuring tank twice as t1 & t2.if difference exceeds 10% take third reading which comes within the range

3. Bring the hook gauge at the Vena Contracta and note x and y.

4. Close the drain gate valve of the collecting tank and note the time for say, 5cm rise in the tank

5. Repeat the experiments for various head and tabulate observations.

Tabulation

Co-ordinate at the Vena Contracta in X direction = -------m

Co-ordinate at the Vena Contracta in Y direction = -------mSl.Nohead of

Water H cmX1

cmY1

cmX1-X0Y1- Y0Time for h in cm rise of water in t sec Actual discharge

Qa m3/secTheoretical dischargeQt

m3/s CvCc

Sample Calculation

Hook gauge headings at Vena Contracta X0 = --------- m

Y0 = ---------- m

Time for h cm rise of water = ---------sec

Qa (Actual discharge)= (Area of tank x h) / time =(A x h)/t m3/sec

Qt (theoretical discharge)=a x(2gh)

Coefficient of discharge, Cd = Qa / QtResult

The values of hydraulic coefficients Cd = --------

Inference

11. Study of losses in pipe flow-major lossesAim:

To study the flow in pipes and determine the losses due to pipe friction, Darcys coefficient and Chezys co-efficient of friction for the given pipe. Apparatus:Experimental setup such as pipelines, manometer, collecting tank, stopwatch and scale.

Specifications:-

Length of the pipe L = --------cm

Diameter of the pipe D = --------cm

Area of the collecting tank A = -------cm2

Principle:Due to pipe friction, there will be head loss and is denoted by Hf for a known pipe length

of L.

Head loss, Hf = 4fLV2/(2gD) cm (Darcy-Weisbach Eqn)The actual discharge Qa through the pipe is determined by noting the time for collecting x cm rise of water, Qa = A(x/t) c.c/sec.

A = Area of the collecting tank.

t = Time to collect x cm of water.

V=Qa /((D2/4) cm/sec.

D = Diameter of the pipe through which fluid flows

L = Length of the pipe.

By noting Hf from the manometer, Darcys coefficient of friction can be calculated.

Hf = X x12.6 cm of water.

X = Manometer pressure difference in cm of Hg.Chezys co.efficient V=C

m=hydraulic mean radius

i= loss of head per unit length i.e. H/l

Procedure:1. Select the pipe and make sure the fluid is flowing only through this pipe.

2. Open the manometer cocks on this pipe.

3. Allow the water through the pipe at maximum opening of the valve and note the head difference X in the manometer.

4. Adjust the outlet valve to get the required pressure difference in the manometer.

5. Note the time in seconds to collect x cm rise of water in the collecting tank.

6. Repeat the experiment for different flow rate.

7. Do the above experiment for the second pipe also.

Tabulation: SlNoManometer readings in cmTime for X cm rise of water t secQa= AX

t

cm3/secV= Qa

( d2 /4

cm /s

F =

Hf g d

2 L V2

ReNo = (vd

( V2 2g

cm

H1cm left sideH2 cm right sideH=H2-H1 cm

SAMPLE CALCULATION

Result: Inference

12. udy of losses in pipe flow- minor lossesAim:

To study the flow in pipes and to determine the minor losses due to coefficient of pipe fittings and loss of head (Bend, Elbow, Sudden expansion and sudden contraction)

Apparatus:

Experimental setup such as pipelines, manometer, collecting tank, stopwatch and scale.

Specifications:

Diameter of the pipe D = --------cm

Area of the collecting tank A = -------cm2

Principle:

The loss of head in the various pipe fittings like Bend & Elbow is generally given by

HL = k V2 /2g

Where V =mean velocity of flow in the pipe.

k = coefficient of pipe fitting.

The actual discharge Qa through the pipe is determined by noting the time for collecting x cm rise of water, Qa = Ah/t c.c/sec.

A = Area of the collecting tank.

t = Time to collect h cm of water.

V=Qa /((D2/4) cm/sec.

D = Diameter of the pipe through which fluid flows

In case of sudden expansion the loss of head is given by

He = k (V1 V2)2 / 2g

V1 = velocity of flow before expansion (smaller pipe)

V2 = velocity of flow after expansion. (Bigger pipe)

In case of sudden contraction the loss of head is given by

Hc = k V22 /2g

V2 = velocity of flow after contraction. (Smaller pipe)

By noting HL from the manometer, coefficient of pipefitting can be calculated.

HL = X x12.6 cm of water.

X = Manometer pressure difference in cm of Hg.

Procedure: 1. Select the pipe and pipefitting and make sure the fluid is flowing only through this pipe.2. Open the manometer cocks only for the selected pipefitting.3. Allow the water through the pipe at maximum opening of the valve and note the head

difference X in the manometer. 4. Adjust the outlet valve to get the required pressure difference in the manometer.5. Note the time in seconds to collect x cm rise of water in the collecting tank.6. Repeat the experiment for different flow rate.7. Do the above experiment for the other pipefitting also.Tabular columnExpManometer readinghead loss

time for 10 cm rise

dischargevelocityVelocity

co-efficientLoss co-efficientMean

H1H2

bend

elbow

sudden expansion

sudden contractiOn

SAMPLE CALCULATION

Result:

Inference

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