1. Enrollment No: 141120105025 141120105029 141120105036 141120105040 1 Subject: Fluid Flow Operations (2130502) Department of Chemical Engineering Pacific School of Engineering, Surat

2. Fluids can move or flow in many ways. Water may flow smoothly and slowly in a quiet stream or violently over a waterfall. The air may form a gentle breeze or a raging tornado. To deal with such diversity, it helps to identify some of the basic types of fluid flow. 2

3. 3  Laminar vs. turbulent flow.  Laminar flow: fluid particles move in smooth, layered fashion (no substantial mixing of fluid occurs).  Turbulent flow: fluid particles move in a chaotic, “tangled” fashion (significant mixing of fluid occurs).  Steady vs. unsteady flow.  Steady flow: flow properties at any given point in space are constant in time, e.g. p = p(x,y,z).  Unsteady flow: flow properties at any given point in space change with time, e.g. p = p(x,y,z,t).

4. 4 Newtonian (low μ) Newtonian (high μ) Bingham-plastic 00 cc Casson fluid Pseudo-plastic (shear-thinning) Dilatant (shear-thickening) Strain rate (1/s)  (Pa)  Newtonian fluids: water, air.  Pseudoplastic fluids: paint, printing ink.  Dilatant fluids: dense slurries, wet cement.  Bingham fluids: toothpaste, clay.  Casson fluids: blood, yogurt.  Visco-elastic fluids: polymers (not shown in graph because viscosity is not isotropic).

5. 5  Incompressible vs. compressible flow.  Incompressible flow: volume of a given fluid particle does not change.  Implies that density is constant everywhere.  Essentially valid for all liquid flows.  Compressible flow: volume of a given fluid particle can change with position.  Implies that density will vary throughout the flow field.  Compressible flows are further classified according to the value of the Mach number (M), where.  M < 1 - Subsonic.  M > 1 - Supersonic.

6. 6  Single phase vs. multiphase flow.  Single phase flow: fluid flows without phase change (either liquid or gas).  Multiphase flow: multiple phases are present in the flow field (e.g. liquid-gas, liquid-solid, gas-solid).  Homogeneous vs. heterogeneous flow.  Homogeneous flow: only one fluid material exists in the flow field.  Heterogeneous flow: multiple fluid/solid materials are present in the flow field (multi-species flows).

7. In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity at a point in the fluid changes as time passes. 7

8. Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast-moving fluid. In turbulent flow, the velocity at a point changes erratically from moment to moment, both in magnitude and direction. 8

9. Most liquids are nearly incompressible; that is, the density of a liquid remains almost constant as the pressure changes. To a good approximation, then, liquids flow in an incompressible manner. In contrast, gases are highly compressible. However, there are situations in which the density of a flowing gas remains constant enough that the flow can be considered incompressible. 9

10. A viscous fluid, such as honey, does not flow readily and is said to have a large viscosity. In contrast, water is less viscous and flows more readily; water has a smaller viscosity than honey. The flow of a viscous fluid is an energy-dissipating process. A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. Although no real fluid has zero viscosity at normal temperatures, some fluids have negligibly small viscosities. An incompressible, nonviscous fluid is called an ideal fluid. 10

11. When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles. A streamline is a line drawn in the fluid such that a tangent to the streamline at any point is parallel to the fluid velocity at that point. Steady flow is often called streamline flow. 11

12. (a)In the steady flow of a liquid, a colored dye reveals the streamlines. (b) A smoke streamer reveals a streamline pattern for the air flowing around this pursuit cyclist, as he tests his bike for wind resistance in a wind tunnel. 12

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16. For steady flow, the speed, pressure, and elevation of an incompressible and nonviscous fluid are related by an equation discovered by Daniel Bernoulli (1700–1782). 16

17. In the steady flow of a nonviscous, incompressible fluid of density r, the pressure P, the fluid speed v, and the elevation y at any two points (1 and 2) are related by: 17

18. The tarpaulin that covers the cargo is flat when the truck is stationary but bulges outward when the truck is moving. 18

19. In a household plumbing system, a vent is necessary to equalize the pressures at points A and B, thus preventing the trap from being emptied. An empty trap allows sewer gas to enter the house. 19

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22. 22  The Reynolds number Re is defined as: Re =  V L / m.  Here L is a characteristic length, and V is the velocity.  It is a measure of the ratio between inertial forces and viscous forces.  If Re >> 1 the flow is dominated by inertia.  If Re << 1 the flow is dominated by viscous effects.

23. 23 Re = 0.05 Re = 10 Re = 200 Re = 3000

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