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FLUID MECHANICS FOR CHEMICAL ENGINEERS

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Introduction Fluid mechanics, a special branch of general mechanics, describes the laws of liquid and gas motion. Flows of liquids and gases play an important role in nature and in technical applications, as, for example, flows in living organisms, atmospheric circulation, oceanic currents, flows in rivers, wind- and water loads on buildings and structures, gas motion in flames and explosions, aero- and hydrodynamic forces acting on airplanes and ships, flows in water and gas turbines, pumps, engines, pipes, valves, bearings, hydraulic systems, and others. The Fluid Mechanics is essential in Chemical Engineering because the majority of chemical – processing operations are conducted either partly or totally in the fluid phase. Examples of such operations abound in the Biochemical, chemical, energy, fermentation, materials, petroleum, pharmaceutical, polymers and waste-processing industries. So what is a Fluid? A fluid is defined as a substance that deforms continuously whilst acted upon by any force tangential to the area on which it acts. Such a force is termed a shear force, and the ratio of the shear force to the area on which it acts is known as the shear stress. The rate at which the fluid deforms continuously depends not only on the magnitude of the applied force but also on a property of the fluid called its viscosity or resistance to deformation and flow.

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Pressure Pressure Force per unit area is called pressure, and its unit is the Pascal, N/m2 in the SI system and psia, lbf/in2 absolute, in the English system. Force per unit area is called pressure, and its unit is the Pascal, N/m2 in the SI system and psia, lbf/in2 absolute, in the English system.

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The pressure used in all calculations of state is the absolute pressure measured relative to absolute zero pressure. However, pressures are often measured relative to atmospheric pressure called gage or vacuum pressures. In the English system the absolute pressure and gage pressures are distinguished by their units, psia (pounds force per square inch absolute) and psig (pounds force per square inch gage), respectively; however, the SI system makes no distinction between absolute and gage pressures. The pressure used in all calculations of state is the absolute pressure measured relative to absolute zero pressure. However, pressures are often measured relative to atmospheric pressure called gage or vacuum pressures. In the English system the absolute pressure and gage pressures are distinguished by their units, psia (pounds force per square inch absolute) and psig (pounds force per square inch gage), respectively; however, the SI system makes no distinction between absolute and gage pressures.

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The relation among atmospheric, gage, and vacuum pressures is shown below. Small to moderate pressure differences are measured by a manometer and a differential fluid column of height h corresponds to a pressure difference between the system and the surroundings of the manometer. This pressure difference is determined from the manometer fluid displaced height as

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Velocity If the fluid passes through a plane of area A normal to the direction of the velocity,, the corresponding volumetric flow rate of fluid through the plane is Q =u A. If the fluid passes through a plane of area A normal to the direction of the velocity,, the corresponding volumetric flow rate of fluid through the plane is Q =u A. The corresponding mass flow rate is m= p Q = p u A, where p is the (constant) fluid density. The corresponding mass flow rate is m= p Q = p u A, where p is the (constant) fluid density. When velocity is multiplied by mass it gives momentum, a quantity of prime importance in fluid mechanics. The corresponding momentum flow rate passing through the area A is M = mu = p u 2 A. When velocity is multiplied by mass it gives momentum, a quantity of prime importance in fluid mechanics. The corresponding momentum flow rate passing through the area A is M = mu = p u 2 A.

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Basic laws. When applying these laws, the procedure is first to identify a system, its boundary, and its surroundings; and second, to identify how the system interacts with its surroundings. Refer to Fig. and let the quantity X represent either mass, energy, or momentum. When applying these laws, the procedure is first to identify a system, its boundary, and its surroundings; and second, to identify how the system interacts with its surroundings. Refer to Fig. and let the quantity X represent either mass, energy, or momentum.

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Density S= p/ p w S= p/ p w Degrees A.P.I. (American Petroleum Institute) are related to specific gravity s by the formula Degrees A.P.I. (American Petroleum Institute) are related to specific gravity s by the formula A.P.I= 141.5/S -131.5 A.P.I= 141.5/S -131.5 Thus, for the crude oil listed in Table 1.1, indeed gives 141.5/0.851 — 131.5 = 35°A.P.I.

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Densities of gases. For ideal gases, pV nRT, where p is the absolute pressure, V is the volume of the gas, n is the number of moles, R is the gas constant, and T is the absolute temperature. If M is the molecular weight of the gas, it follows that: Densities of gases. For ideal gases, pV nRT, where p is the absolute pressure, V is the volume of the gas, n is the number of moles, R is the gas constant, and T is the absolute temperature. If M is the molecular weight of the gas, it follows that: p= PM/RT p= PM/RT For NON ideal gases For NON ideal gases p= PM/ZRT p= PM/ZRT

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VISCOSITY All fluids offer resistance to any force tending to cause one layer to move over another. Viscosity is the fluid property responsible for this resistance. Since relative motion between layers requires the application of shearing forces, that is, forces parallel to the surfaces over which they act, the resisting forces must be in exactly the opposite direction to the applied shear forces and so they too are parallel to the surfaces.

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SURFACE TENSION Surface tension arises from the forces between the molecules of a liquid and the forces (generally of a different magnitude) between the liquid molecules and those of any adjacent substance.

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Units An important component to the solution to any engineering thermodynamic problem requires the proper use of units.

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