Aim: To determine a relation between friction factor and Reynolds number for flow through circular pipe.
Apparatus:Three pipe assembly with two presssure tappings in each pipe,manometer with CCl_{4} as a manometric fluid, stopwatch, measuringtank.
Theory:
Friction losses are a complex function of the system geometry, the fluid properties and the flow rate in the system. By observation, the head loss is roughly proportional to the square of the flow rate in most engineering flows (fully developed, turbulent pipe flow). This observation leads to the DarcyWeisbach equation for head loss due to friction:
which defines the friction factor, f. f is insensitive to moderate changes in the flow and is constant for fully turbulent flow. Thus, it is often useful to estimate the relationship as the head being directly proportional to the square of the flow rate to simplify calculations.
Reynolds Number is the fundamental dimensionless group in viscous flow. Velocity times Length Scale divided by Kinematic Viscosity.
Relative Roughness relates the height of a typical roughness element to the scale of the flow, represented by the pipe diameter, D.
Pipe Crosssection is important, as deviations from circular crosssection will cause secondary flows that increase the pressure drop. Noncircular pipes and ducts are generally treated by using the hydraulic diameter,
in place of the diameter and treating the pipe as if it were round.
For laminar flow, the head loss is proportional to velocity rather than velocity squared, thus the friction factor is inversely proportional to velocity.
Geometry Factor k 

Square 
56.91 
2:1 Rectangle 
62.19 
5:1 Rectangle 
76.28 
Parallel Plates 
96.00 
The Reynolds number must be based on the hydraulic diameter. Blevins (table 62, pp. 4348) gives values of k for various shapes. For turbulent flow, Colebrook (1939) found an implicit correlation for the friction factor in round pipes. This correlation converges well in few iterations. Convergence can be optimized by slight underrelaxation.
The familiar Moody Diagram is a loglog plot of the Colebrook correlation on axes of friction factor and Reynolds number, combined with the f=64/Re result from laminar flow.
An explicit approximation
provides values within one percent of Colebrook over most of the useful range.
Procedure:
(1) Maintain constant overflow for constant head pressure & steady flow.
(2) Connect the manometer to the two pressure tappings of the pipe.
(3)Make it sure that there are no air bubbles in the tapping lines.
(4)Ensure that manometer indicates zero reading at no flowthrough the pipe line.
(5) Open the valve to a certain opening & Wait till the flow is stabilized. This is indicated by the steady levels of the manometric fluid in the limbs of the manometer.
(6) Note down the manometer readings.
(7) Measure the flow rate of water by collecting it in a measuring tank, either for a known period of time or for a known volume.
(8) Repeat (3), (4) ,(5),(6) and (7) to obtain atleast eight to ten evenly spaced readings. The last reading should preferably be takenat the maximum possible manometer reading.
(9) Repeat above procedure for same dia. as first assembly but different material of construction.
(10) Repeat above procedure for same material of pipe as set – II but larger in diameter.
Graph:
Plot the graph of F_{obsr.} vs N_{Re} on the loglog graph paper. On the same graph paper plot the F_{theo.} vs N_{Re.}
(Since the expression for friction factor is in general of the form
f = A(N_{Re})^{_b} taking log on both sides leads to an expression.
log(f) = logA – b log (N_{Re})
Which is an equation of straight line with a slope of (b) (the power of Reynolds number)
Result:
Comment on the nature of graph actually obtained & the theoritical relation between F & N_{Re.}
Conclusion:______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
(2) Density of water at ___ °c, ρ = _____ kg/m^{3}
(3) Viscosity of water at ___ °c, μ = ____ kg/m*sec
(4) Density of CCl_{4} , ρ = _______ kg/m^{3}
(5) Inside dia. of set – II = _______ mm
(6) ‘’ ‘’ ‘’ setIII = _______ mm
(7) ‘’ ‘’ ‘’ set – I = ______ mm
(8) Centre to centre distance betn. two tappings for each set, L
For set – I = _________ mt.
or set – II &III = _________mt.
Observation Table:
Sr. No. 
Manometer reading ,Rm = h_{1} – h_{2} mt 
Volume of water collected, m^{3} 
Time for collection of water t, sec 
Water flow rate , Q = m^{3}/sec 
1 

2 

3 

4 

5 

6 
Table of calculated results:
Sr. No 
Head loss due to friction, kg/m^{2}, ΔHf 
Average velocity of water, u, mt/sec 
Reynolds number, N_{Re} =D v ρ/μ 
Obs. value of friction factor f_{obs.} 
Theo. value of friction factor, f_{theo.} 
1 

2 

3 

4 

5 

6 
Model Calculation:
(1) Cross sectional area of pipe, A = ∏/4 ( D_{i} ) ^{2} = __m^{2}
(2) Volumetric flow rate, Q = Volume collected / time = ____ m^{3}/sec
(3) Press. drop due to friction, ΔH_{f} = R_{m×} (ρ_{Ccl4} – ρ_{H2o}) = _____ kg/m^{2}
(4) Average Velocity, u = Q/A = _____ m/sec
(5) Reynolds number, N_{Re} = Duρ/μ= Dimensionless
(6) Obs. value of friction factor, f_{obs.} = ( ΔH_{f} . gc. D) / 2L u^{2} ρ
( Dimensionless)
(7) Theo. value of friction factor, f_{theo.} = 16/ N_{Re(}For N_{Re} < 2100)
(8) Theo. value of friction factor, f_{theo.} = 0.046 (N_{re})^{0.2}
For 4000 < N_{Re} < 100,000
Note : Same calculation for set II & III
(9) Theo. value of friction factor f_{theo.} for smooth tube.
1 /(f/2)^(0.5) = 2.5 ln (N_{Re} (f/8)^(1/2)) + 1.75 ( pvc pipe)
1) Roughness has________ effect on the friction factor for laminar flow when k is very small.
very high
ha ha ha…..
low
more
exponential
more
no
more
2)A flange with no opening is called_______.
Unique
Not defined
blind
ha ha ha…..
oneway
it is closure.
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