Aim: To obtain relation between modified friction factor and Reynolds number for flow of fluid through a packed-bed.
Apparatus: 1) A Packed column with two pressure tappings
2) Manometer (with ccl4 as manometric fluid).
3) Stop-watch
4) Measuring tank
Theory:
Consider a porous medium consisting of sand or some porous rock or glass beads or cotton cloth contained in a pipe. At any one cross section perpendicular to the flow, the average velocity may be based on the entire cross sectional area of pipe, in which case it is called the superficial velocity V_{s}
Or it may be based on the area actually open to the flowing fluid, in which case it is called the interstitial velocity V_{I}
Where e is the porosity or void fraction.
Therefore,Hydraullic radius;
i.e.
i.e.
h_{f} = Dp / r = 2fLV_{I}^{2} / D_{e}
substituting for V_{I} in terms of V_{S}
i.e. V_{I }= V_{S} / e
NRe = D_{e} V_{I }r / m
Substituting for D_{e} and V_{I}
As in the case of flow in pipes, there are several different friction factors in common usage for flowing in porous media, all differing by a constant.
Experimental data indicate that the constant is about 150, so that for laminar flow we find experimentally,
f_{PM = }150 / NRe_{PM}
i.e.
This equation is called as as Kozeny-Carman equation. It is valid for NRe_{PM} less than about 10.
Turbulent flow:
f_{PM} = 1.75 (experimental value)
Therefore,
This is the Burke-Plummer equation, valid for NRe_{PM} greater than 1000
Since there is a smooth transition from all-laminar to all-turbulent flow, Ergun showed that if we add the friction factor term,
f_{PM} = 1.75 + 150 / NRe_{PM}
the transition regions data are predicted reasonably well.
i.e.
This is the Ergun’s equation.
For non-spherical particle Ergun equation is given by,
Procedure:
(1) Connect the manometer to the two pressure tappings of the packed-column. Make it sure that there is no air bubble trapped in the tapping lines. Ensure that manometer indicates zero reading for zero flowrate through the packed-bed.
(2) Open the inlet valve to a certain valve opening and wait till the flow is stabilized. This is indicated by the steady levels of manometric fluid in the limbs of the manometer.
(3) Note down the manometer readings.
(4) 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.
(5) Repeat (2) , (3) and (4) to obtain atleast 10 evenly spaced readings. The last reading should be taken at the maximum permissible flow ( or maximum possible manometer reading ) through the packed-bed.
Graph:
Plot the graph of friction factor versus Reynolds number on the log-log graph paper. On the same graph paper plot theoretical value of friction factor versus Reynolds number. Also plot the graph of Head developed vs Velocity.
Results:
Conclusion:
Observations:
(1) Dia. of particle D_{p} = ______ mt
(2) Dia. of Packed bed, D = _______ mt
(3) Length of packed column, L = _______ mt
(4) Temp. of water ____°C.
(5) Density of water at _____°C, ρ= _______ kg/m^{3}
(6) Viscosity of water at _____°C, μ = ______ kg/msec
(7) Density of mercury, ρ_{m} = ______ kg/m^{3}
(8) Porosity ε = _______
Observation Table:
Sr. No. |
Manometer reading, Rm=h_{1} – h_{2}mt |
Volume of water collected,m^{3} |
Time for collection of water , tsec |
Water flow rate, Q = m^{3}/sec |
Head loss due to friction, ΔH_{f}mt |
1 |
|||||
2 |
|||||
3 |
|||||
4 |
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5 |
|||||
6 |
Table of Calculated Results:
Superfacial velocity , us= m/sec |
u = u_{s} / ε |
N_{Re} = D_{p}u_{sρ}μ |
Modified Rey. No.N_{Re’}= N_{Re}_{/}1-ε |
Modified friction factor, f‘ = ΔH_{f}. gc.D_{p} ε^{3}L. u_{s}^{2} (1-ε) |
Model Calculation:
(1) Head loss due to friction, DH_{f} = Rm ( ρ_{m} – ρ_{H2O} )/ ρ_{H2O} (mt)
(2) Area, A = ∏/4 (D^{2}) (m^{2})
(3) Superfacial velocity, u_{s} = Vol. flow rate / Area = m/sec.
(4) Reynold’s no. N_{Re} = D_{p} u_{s} ρ/μ
(5) Modified Reynold’s no. N_{Re’}^{ }= N_{Re/1-ε}
(6) Modified friction factor, f^{‘} = (ΔH_{f}. gc.D_{p} ε^{3} )/ u_{s}^{2} (1-ε)
(7) Theoritical friction factor, f = 5/ N_{Re} + 0.1/ (N_{Re})^{0.1}
1)Manometers measure the ____________.
difference in pressure
ha ha ha…..
vacuum as well as atmospheric pressure
more
gauge pressure
more
absolute pressure
more
2)k/D ratio defines___________.
diameter
NA
roughness parameter
ha ha ha…..
flow
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