In power correlations for agitated vessels the effect of Froude number appears:
The Weber number can be used to estimate
At very low r.p.m (\(\text {Re}\) less than 5), the power required for agitation is proportional to
At low Reynold’s numbers the power (\(P\)) required for agitating a fluid in a stirred tank becomes independent of inertial forces. In this limit, indicate which of the following relations is satisfied:
\(\text {Po} = P/(\rho N^{3}D^{5})\) :
Power Number
\(\text {Re} = \rho ND^{2}/\mu \) : Reynolds Number
\(N\) is the impeller rotational speed, and \(D\) is the impeller diameter.
1999-1-12-mo For a turbine-agitated and baffled tank, operating at low Reynolds number (based on impeller diameter), the power number \(\text {Po}\) varies with \(\text {Re}\) as
The Power number for a stirred tank becomes constant at high Reynolds number. In this limit, the variation of power input with impeller rotational speed (\(N\)) is proportional to
Match the systems in Group I with equipment used to separate them in Group II.
| Group I | Group II |
|---|---|
| P gas-solid | 1 filter press |
| Q liquid-liquid | 2 cyclone |
| 3 decanter | |
| 4 thickener |
If the frequency of the stirrer in a mixing tank is increased by a factor of 2 while all other parameters are kept constant, by what factor is the power requirement increased at high Reynolds number ?
For a mixing tank operating in the laminar regime, the power number varies with the Reynolds number (Re) as
In a mixing tank operating at very high Reynolds number (\(>10^4\)), if the diameter of the impeller is doubled (other conditions remaining constant), the power required increases by a factor of
A batch bioreactor is to be scaled up from 10 to 10,000 liters. The diameter of the large bioreactor is 10 times that of the small bioreactor. The agitator speed in the small bioreactor is 450 rpm. Determine the agitator speed (rpm) of the large bioreactor with same impeller tip speed as that of the small bioreactor. ____________
To keep the power input constant for a stirred vessel operating under fully developed turbulent flow conditions (constant power number), if the impeller diameter is increased by 20%, the impeller speed should be decreased by a factor of
The mixing of rubber latex solution was studied in an unbaffled mixer in the laboratory. The mixer was equipped with a six blade turbine impeller. A tyre company scales this process up using a baffled tank. The baffled tank has 3 times the diameter of the lab scale mixer. It uses the same type of impeller operated at the same speed. The relevant shape factors are also the same. Assuming that laminar conditions prevail in both cases, the power requirement in the industrial scale mixer.
Consider the scale-up of a cylindrical baffled vessel configured to have the standard geometry (i.e. Height = Diameter). In order to maintain an equal rate of mass transfer under turbulent conditions for a Newtonian fluid, the ratio of the agitator speeds should be (Given: \(N_1, D_1\) are agitator speed and vessel diameter before scale-up; \(N_2, D_2\) are agitator speed and vessel diameter after scale-up)
An agitated cylindrical vessel is fitted with baffles and flat blade impellers. The power number for this system is given by \(\displaystyle N_P=\frac {P}{\rho n^3D_a^5}\) where \(P\) is the power consumed for the mixing, \(\rho \) is the density of the fluid, \(n\) is the speed of the impeller and \(D_a\) is the diameter of the impeller. The diameter of the impeller is 1/3\(^{\text {rd}}\) the diameter of the tank and the height of liquid level is equal to the tank diameter. The impeller speed to achieve the desired degree of mixing is 4 rpm. In a scaled up design, the linear dimensions of the equipment are to be doubled, holding the power input per unit volume constant. Assuming the liquid to be Newtonian and \(N_P\) to be independent of Reynolds number, what is the impeller speed (in rpm) to achieve the same degree of mixing in the scaled up vessel?
An agitated baffle vessel is being used to prepare a uniform solution of viscosity 2 cP, running the agitator at 100 rpm, so as to obtain a Reynolds number of 50,000. If the contents of the vessel are replaced by a solution of viscosity 4 cP, and the
agitator rpm is increased to 200, by how much % will the power requirement increase?
Match the following:
A. \(\displaystyle \Delta p = \frac {32Lu\mu }{D^2}\)
B. \(\displaystyle \frac {P}{T} = K\left [\frac {1}{{D_{vsb}}} - \frac {1}{{D_{vsa}}}\right ] \)
C. \(\displaystyle \frac {P}{n^3D_a^5\rho }\)
D. \(\displaystyle u_t = \frac {gD_p^2(\rho _p-\rho )}{18\mu }\)
Match the following:
| (I) | Kozeny equation | (A) | \(\displaystyle E = K \ln \frac {D_1}{D_2}\) |
| (II) | Hagen-Poiseuille equation | (B) | \(\displaystyle u_t= \left [3d_pg\left (\frac {\rho _p-\rho }{\rho }\right )\right ]^{1/2}\) |
| (III) | Kick’s law | (C) | \(\displaystyle u_t=\frac {gd_p^2(\rho _p-\rho )}{18\mu }\) |
| (IV) | Stokes’ law | (D) | \(\displaystyle E = k\left [\frac {1}{D_2}-\frac {1}{D_1}\right ]\) |
| (E) | \(\displaystyle \Delta P = \frac {32Lu\mu }{D^2}\) | ||
| (F) | \(\displaystyle u = \frac {1}{k}\cdot \frac {\epsilon ^3}{(1-\epsilon )^2}\cdot \frac {1}{\mu S^2}\cdot \frac {\Delta P}{l}\) |
For geometrically similar baffled stirred tanks, the Power number is known to remain constant at high Reynolds number.
A small model reactor is to be built for scale up studies of the behavior of a proposed large industrial stirred tank reactor having 1000 times capacity. The bigger unit of 2 m diameter will have a liquid depth of 2 m. This will be fitted with a four bladed Rushton turbine of 0.6 m diameter.
In an agitated vessel baffles are used to suppress ––––- .
The power required to stir water (density = 1000 kg/m\(^3\), viscosity = 0.001 kg/m.s) in a laboratory experiment with the impeller (diameter = 5 cm, blade width = 1 cm) rotating at 5 rpm is \(10^{-2}\) W. Consider an industrial stirred vessel where a fluid (density = 900 kg/m\(^3\), viscosity = 0.184 kg/m.s) has to be stirred at 1 rpm using an impeller of 1.6 m diameter and 0.32 m blade width.
Show that the laboratory experiment and industrial vessel are geometrically and dynamically similar.
Estimate the power requirements of the industrial vessel.
Last Modified on: 03-May-2024
Chemical Engineering Learning Resources - msubbu
e-mail: learn[AT]msubbu.academy
www.msubbu.in