Fluid flow

1. Fluid flow • A fluid is a substance that flows When subjected to a shearing stress layers of the fluid slide relative to each other Both gases and liquids are defined as fluids

2. Fluid flow is the study of the flow of gases and liquids The degree of resistance to shear stress is represented by the term ‘viscosity’ High viscosity means high resistance to shear stress – does not flow easily

3. viscosity Viscosity-fluid property that influences the rate of fluid flow under stress. y

4. The viscosity is the ratio between the shear stress and the velocity gradient between the plates, or Newton’s Law of Viscosity

5. Units on shear stress and pressure Force/area=mass*length/time2 * 1/area =mass * length/time * 1/time * 1/area = mass*velocity * 1/(time * area) = momentum/(time*area) = momentum flux

6. Flow classifications • 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).

7. 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).

8. Flow classifications • 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.

9. 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). Newtonian (high μ) Bingham-plastic Casson fluid 0 Pseudo-plastic (shear-thinning) c Newtonian (low μ) Dilatant (shear-thickening) Strain rate (1/s) Newtonian vs. non-Newtonian  (Pa)

10. Steady laminar flow • Steady viscous laminar flow in a horizontal pipe involves a balance between the pressure forces along the pipe and viscous forces. • The local acceleration is zero because the flow is steady. • The convective acceleration is zero because the velocity profiles are identical at any section along the pipe.

11. Pascal’s law • Pascal's principle is defined as A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid.

13. Basics Equations for Fluid Flow The continuity equation Q = v.a where v is the velocity (m/s) and a the area available for flow (m2 e.g. cross sectional area of a pipe) and Q is the flowrate (m3/s)

14. Manometer • A manometer is a device used for measure the pressure of a fluid by balancing it with against a column of a liquid.  • Simple manometer • 1.U-Tube manometer • 2. Inverted U-Tube manometers • Differential manometres • Inclined manometers • Micro manometers

15. U-Tube Manometer: It consist a U – shaped bend whose one end is attached to the gauge point ‘A’ and other end is open to the atmosphere. It can measure both positive and negative (suction) pressures. It contains liquid of specific gravity greater than that of a liquid of which the pressure is to be measured.

16. Differential U-Tube Manometer: A U-Tube manometric liquid heavier than the liquid for which the pressure difference is to be measured and is not immiscible with it.

17. Inverted U-Tube Manometer: Inverted U-Tube manometer consists of an inverted U – Tube containing a light liquid. This is used to measure the differences of low pressures between two points where where better accuracy is required. It generally consists of an air cock at top of manometric fluid type.

18. Inclined Manometer: Inclined manometer is used for the measurement of small pressures and is to measure more accurately than the vertical tube type manometer. Due to inclination the distance moved by the fluid in manometer is more.

19. Micro Manometer: Micro Manometer is is the modified form of a simple manometer whose one limb is made of larger cross sectional area. It measures very small pressure differences with high precision.

20. Reynolds number • The Reynolds number Re is defined as: Re = r 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.

21. Effect of Reynolds number Re = 0.05 Re = 10 Re = 200 Re = 3000

22. Bernoullis Theorem • In most flows of liquids, and of gases at low machnumber, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible and these flows are called incompressible flows. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is:

23. here • points 1 and 2 lie on a streamline, • the fluid has constant density, • the flow is steady, and • there is no friction. • Although these restrictions sound severe, the Bernoulli equation is very useful, • partly because it is very simple to use and partly • because it can give great insight into the balance between pressure, velocity and elevation.

25. where: • v is the fluid flow speed at a point on a streamline, • g is the acceleration due to gravity, • z is the elevation of the point above a reference plane, with the positive z-direction pointing upward – so in the direction opposite to the gravitational acceleration, • p is the pressure at the chosen point, and • ρ is the density of the fluid at all points in the fluid. • The constant on the right-hand side of the equation depends only

26. VENTURI METERS.  Venturi meters are flow measurement instruments which use a converging section of pipe to give an increase in the flow velocity and a corresponding pressure drop from which the flowrate can be deduced. They have been in common use for many years, especially in the water supply industry.

28. where β is the diameter ratio, d/D. In reality, there is a small loss of total pressure, and the equation is multiplied by the discharge coefficient, C. where Δp is the differential pressure (≡p1 − p2).

29. Orifice plate An Orifice plate  is a plate with a hole through it, placed perpendicular to the flow; it constricts the flow, and measuring the pressure differential across the constriction gives the flow rate. It is basically a crude form of venturimeter, but with higher energy losses. There are three type of orifice: concentric, eccentric, and segmental.

31. where β is the diameter ratio, d/D. In reality, there is a small loss of total pressure, and the equation is multiplied by the discharge coefficient, C. where Δp is the differential pressure (≡p1 − p2).

32. Pitot-tube A pitot tube is used to measure fluid flow velocity. The tube is pointed into the flow and the difference between the stagnation pressure at the tip of the probe and the static pressure  at its side is measured, yielding the dynamic pressure from which the fluid velocity is calculated using Bernoullis equation. A volumetric rate of flow may be determined by measuring the velocity at different points in the flow and generating the velocity profile.