Lecture 10 - Revision microbes and PowerPoint (1).pptx

microbes class lecturer in the medical field

1. Preparation for the exam Exam format Duration: ONE hour. Number of questions: 2 or 3, varying from year to year. Answer all questions – make sure to write down all steps where calculations are involved. Formula sheets will be provided and these can be downloaded from MyStudies .

2. Preparation for the exam Revisions questions will be provided over the course of next few weeks. Try the tutorial questions in the handout. The sample solutions for the tutorial questions are available online but DO NOT Look at these until you have tried yourself. Try out the revision questions, which are a collection of past exam papers. Try the formative online multiple choice tests. Mock exam on 15 th Dec.; the paper will be uploaded on myStudies after the test.

3. Section 1 - Hydrostatics Basic units in hydraulics: Length in metres (m) Mass in kilograms (kg) Time in seconds (s) For all hydraulic calculations, units must be converted into the metric units if not given as such. E.g., If a pipe diameter is given as 50mm, then use 0.05m If discharge is given a value of 100 l/s, then change it to 0.1 m 3 /s

4. Fundamental properties of fluids Density ( ): kg/m 3 Viscosity Dynamic viscosity ( ) in Ns/m 2 Kinematic viscosity ( ) in m 2 /s  = / 

5. Section 2. Hydrostatics Basic concept of pressure Notation p with units of N/m 2 , or in Pa (Pascal) p is always normal to the solid surface of contact p =  g y y is vertical distance from free surface Pressure force: F =  gl c A sin Point of action

6. Forces on curved surfaces. Horizontal component F x = force on an imaginary vertical plane surface projected from the curved surface Vertical component F y = weight of water above the curved surface =  g x volume Direction is defined in terms of F x & F y Buoyancy or upthrust : F B =  g x displaced volume of liquid Pressure measurements Gauge pressure p Absolute pressure p abs = p + p a

7. Section 3. Hydrodynamics Acceleration due to gravity Flow rate or discharge Notation: Q or q Units: m 3 /s l/s or m 3 /h are often used in problem description, so must be converted into m 3 /s before doing any calculations. Flow velocity Notation: V or u or U Units: m/s Relate to Q: V = Q/A A = cross-sectional area of flow in m 2 .

8. Mass conservation law

9. Energy conservation law Hydraulic energy = pressure + potential + kinetic Bernoulli eq : p/  g + z + u 2 /2g = constant, or p 1 /  g + z 1 + u 1 2 /2g = p 2 /  g + z 2 + u 2 2 /2g Bernoulli eq may applied between any two points connected by the same liquid. Out of 6 variables p 1 , u 1 , z 1 , p 2 , u 2 and z 2 , 5 of them must be known to work out the 6 th unknown. Any point in contact with air: the pressure is p a = 0; Free surface of a reservoir: u = 0;

10. Momentum Eq F x = Q(u 2x – u 1x ) , F y = Q(u 2y – u 1y ), F z = Q(u 2z – u 1z ) F x , F y & F z are net forces in each direction and are made up of the reaction and pressure forces in each direction u x , u y , u z are velocity components in x, y & z direction.

11. Boundary layer theory: “No-slip” condition Friction within liquid due to viscosity The friction is known as shear stress in N/m 2 Viscous effects lead to Non-uniform flow velocity Hydraulic energy loss Section 4. Real fluids

12. Reynolds number and states of flow: Re = UD/  Laminar flow: Re < 2000 Turbulent flow: Re > 4000 Transitional flow: Re = 2000 ~ 4000 Boundary layer characteristics There is a velocity gradient The velocity increases as the distance from the solid surface increases These is a laminar sub-layer inside the boundary layer, which is attached to the solid surface and is laminar Notations: Boundary layer thickness ; and laminar sub-layer thickness ’

13. Surface roughness Notation: k s Describes the mean height of surface imperfection or irregularities Surface roughness k s versus laminar sub-layer thickness ’ k s < ’: laminar sub-layer covers the surface imperfections and the boundary layer is unaffected, creating a “hydraulically smooth boundary” k s > ’: laminar sub-layer is broken by surface imperfections and the boundary layer is affected, creating a “hydraulically rough boundary”

14. Flow separation Associated with bluff bodies, i.e., tall buildings, bridge piers, airfoils There is a vortex wake downstream of the bluff body The vortex motion leads to an oscillating drag force The oscillating drag can lead to “fatigue” failure of a structure.

15. Estimation of head loss in pipe flow Head loss ( h f ) in a pipe flow refers to the amount of hydraulic energy being converted into heat due to friction For a pipe of diameter D and length L: C-W Eq for friction factor l : , Bar’s Eq :