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**BIO 208 FLUID FLOW OPERATIONS IN BIOPROCESSING [ 3 1 0 4 ]**

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**SYLLABUS Fluid statics Fluid dynamics Bernoulli’s equation**

Hagen Poiseuille's equation Friction factor Flow past immersed bodies Flow thro bed of solids Fluidization Transportation and metering of fluids Mixing & Agitation

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References….. Unit Operations of Chemical Engineering, 5th edn., McCabe & Smith. Chemical Engineering, Vol. I, Coulson and Richardson Introduction to Chemical engineering, Badger and Banchero Unit Operations, Foust et. al.,

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**Why?????? Fluid mechanics is an important area of engg. science.**

The nature of flow in pipes and reactors depends on the power input to the system & physical characters of fluid In fermentors, fluid properties affect process energy requirements & effectiveness of mixing which can have dramatic influence on productivity & the success of equipment scale-up. Transport of heat and mass is often coupled with fluid flow. Fluids in bioprocessing often contain suspended solids, consist of more than one phase, and have non-Newtonian properties. All of these features complicate analysis of flow behavior and present many challenges in bioprocess design.

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FLUID…… A fluid may be defined as a substance that does not permanently resist distortion and, hence, will change its shape. In this text gases, liquids, and vapors are considered to have the characteristics of fluids and to obey many of the same laws. In the process industries, many of the materials are in fluid form and must be stored, handled, pumped and processed. So it is necessary that we become familiar with the principles that govern the flow of fluids and also with the equipment used. Typical fluids encountered include water, air, CO2, oil, slurries, and thick syrups & BIOPRODUCTS

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**Compressible & Incompressible**

If a fluid is inappreciably affected by changes in pressures it is said to be incompressible. Most liquids are incompressible. Gases are considered to be compressible fluids.

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Momentum Transfer The study of momentum transfer, or fluid mechanics as it is often called, can be divided into two branches; fluid statics, or fluids at rest, and fluid dynamics or fluids in motion. Since in fluid dynamics momentum is being transferred, the term “momentum transfer” or “transport” is usually used.

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Viscosity The viscosity (m) of a fluid measures its resistance to flow under an applied shear stress. Representative units for viscosity are kg/(m.sec) g/(cm.sec) (also known as poise designated by P) The centipoise (cP), one hundredth of a poise, is also a convenient unit

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**The kinematic viscosity (n) is the ratio of the viscosity to the density:**

n = m/r, Has the units of m2/s

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**Viscosity of liquids: Viscosity of gases: @ 25oC, mwater = 1 cP and**

Viscosity of liquids in general, decreases with increasing temperature. Viscosity of gases: Viscosity of gases increases with increase in temperature. @ 25oC, mwater = 1 cP and mair = 1 x 10-2 cP

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Fluid Statics…… In fig., a stationary column of fluid of ht h2 and constant CSA A, where A=Ao=A1=A2, is shown. The pressure above the fluid is Po (which could be the press of atmos above the fluid) Also for a fluid at rest, the force/unit area (ie Pressure) is the same at all points with the same elevation. Pressure in a static fluid

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We know F = mg and P = F/A Total mass of fluid = h2 A r F=h2A r g P = F /A = h2 r g This is the press on A2 due to the mass of fluid above it. To get the TOTAL PRESS P2 on A2, the Po must be added P2 = h2 r g + Po To cal P1, P1 = h1r g + Po The press difference bet 2 and 1 is DP = P2-P1 = (h2 – h1)r g

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Since it’s the vertical height of a fluid that determines the press of fluid, the shape of the vessel doesn’t affect the pressure In the above fig the press P1 at the bottom of all three vessels is the same and equal to h1r g + Po

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Prob 1 A large storage tank contains oil having a density of 917 kg/m3.The tank is 3.66 m tall and is vented (open) to the atmosphere of 1 atm abs at the top. The tank is filled with oil to a depth of 3.05 m (10 ft) and also contains 0.61 m (2.0 ft) of water in the bottom of the tank. Calculate the pressure in Pa and 3.05 m from the top of the tank and at the bottom.

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**Soln…… P1 = Po + (hrg)oil P2 = P1 + (hrg)water = 1.347 x 105 Pa**

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Head of a fluid Expressing the pressure in terms of head in m or ft of a particular fluid We know….P = hrg h = P / rg

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Prob 2 Compare the column heights of water,CCl4(r=1.59 g/cc) and mercury (r=13.65 g/cc) corresponding to a pressure of 50kPa hwater = 5.1m h CCl4 = 3.21m hHg = 0.373m

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