UKSSSC- Fluid Mechanics

INTRODUCTION

Fluid mechanics has a wide range of applications in mechanical and chemical engineering, in biological systems, and in astrophysics. Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. The basic fluid mechanics principles are the continuity equation (i.e. conservation of mass), the momentum principle (or conservation of momentum) and the energy equation. Here I will explain on the expects of UKSSSC/UKPSC Exam Only.

Focus point are-

♀ About Fluid
♀ Properties
♀ Pressure and application
♀ Flow & Hydraulic Energy
♀ Notch & Weir
♀ Flow through pipe

📝CHAPTER-1: FLUIDS

Fluids are defined into two board categories are-

1- Ideal Fluid
2- Real Fluid

1- Ideal Fluid- Ideal fluid are Imaginary fluids having no viscosity, no surface tension and incompressible by nature. Air and water are the example of Ideal Fluid.

2- Real Fluid- Fluids having viscosity, surface tension and compressible. Real fluid are defined in following four categories are-

A- Newtonian- Obey the newton law of viscosity. Newton state that the shear stress is directely proportion to shear strain or angular deformation.

τ = μ(dv/dy)

B-Non Newtonian- doesn't obey the newton law of viscosity.

τ = μ(dv/dy)^n

C- Plastic- Ideal plastic has a definite yield stress. Leaner relation between shear stress and angular deformation also developed in plastic fluid.

τ = c+μ(dv/dy)

D- Elastic- Property of expanding in all the direction even after removing external pressure. Ex.-air,stream and other gases.

📝CHAPTER-2: PROPERTIES OF FLUID

◆ Mass Density(ρ)- mass density defined as the ration of Mass (M) to total Volume (V)

ρ =M/V kg/m^3

◆ Specific Weight(w)- defined as the ration of total weight(W) to total volume (V)

w =W/V kg/m^3

◆ Specific Volume(v) - specific volume is inversely proportional to specific weight or the ration of total volume to total weight.

v = 1/w or V/W m^3/kg

◆ Specific gravity (s) - it is defined as the ration of density of fluid to density of water. Also known as relative density.

s = ρ of fluid / ρ of water , unitless quantity

◆ Viscosity = The resistance between the fluid layers. Viscous fluid obey the newton law of viscosity also. viscosity denoted by μ

S.I unit - N-s/ m^2
C.G.S unit - Poise

👉If temperature is rise, the viscosity of liquid is decrease but the viscosity of gas increase.

👉 If temperature is rise, density and surface tension both are decrease for liquid and gas.

◆ Kinematic Viscosity- it is the ratio of dynamatic viscosity to density of fluid.

S.I unit - m^2/sec
C.G.S - stoke

◆ surface tension- surface tension act as an perpendicular to plane and occurs layer to layer of fluid. Unit is N/m

Drop surface tension = ρπ/2

👉 Relative motion b/w adjacent or neighbouring fluid lager is equal to zero.

◆ Capillarity rise- A small tube phenomenon to rise the water level. The meniscus is the curve in the upper surface of a liquid close to the surface of the container or another object, caused by surface tension.

h = 4σ CosΦ /w.d
w= weight density N/m^3
d = dia of capillarity tube
Φ = Angle of contact to water surface in ℃

👉Pressure head of liquid h= p/w

◆ Compressibility- it is inversely proportional to bulk modulus (k), k = σ/£v, unit of compressibility is mm^/N

📝CHAPTER-3: MEASUREMENT OF PRESSURE

◆ Pascal's law- The Intensity of pressure at any point of a fluid at rest is the same in all directions.

Px =Py =Pz

👉 Pressure always act normal to plane

👉 Pressure intensity varies with the depth of liquid.

👉 Pressure height  above of the free surface at point is called static head.

👉 Hydraulic pressure w =F/a ×A
Here a = area of plunger, A= area of RAM

SI unit of pressure - m^2/second
C.G.S unit - Pascal

◆ Lock gate-  A gate for opening or closing a lock in a canal, or sometimes in a river. A lock is a device used for raising and lowering boats, ships and other watercraft between stretches of water of different levels on river and canal waterways. Lock gate equation-

P = R +F
R= reaction at the upper and bottom hinged
F= force exerted by gate
P= water pressure on gate
RsinΦ = FsinΦ , R = F
Therefore P = RsinΦ or 2FsinΦ, R=F=P/2sinΦ

◆ Types of Pressure-
I)- Atmospheric Pressure
II)- Gauge Pressure
III)- Vacuum Pressure

1- Atmospheric Pressure- Pressure exerted by the envelope of air surrounding the earth surface. Atmospheric pressure measured by the barometers, so called barometric pressure also.This pressure act in normal direction.

Atm.pressure of mercury = 760mm
Atm.pressure of water = 10.34 m
Atm.pressure of sea water = 103 Kn/m^2
Atm.pressure of bars = 1.01325 bar

2- Gauge Pressure- The pressure above from Atmospheric pressure is called Gauge pressure or positive pressure.

3- Vacuum Pressure- The pressure below from Atmospheric pressure is called Vacuum pressure or negative pressure.

◆ Absulote pressure-
● Atmospharic Pressure + Gauge Pressure
● Atmospheric Pressure - Vacuum Pressure

👉 Mercury used in manometer for hight pressure in liquid and low pressure in vapour.

👉 At 20℃ the vapour pressure of mercury is - 1.6×10^-3 N/mm^2

👉 When the pressure is measured above absolute zero is called Absolute pressure.

👉 All pressure gauge raed when open to atmosphere is Zero.

◆ Measurement of pressure- In the fluid mechanics, two types of instrument are used for measuring the pressure-

I)- Manometers

II)- Mechanical Gauges

1- Manometers- Manometer are further classified into two categories are -

A- Simple manometer
B- Differential manometer (not explain)

A- simple manometer- simple manometer also have a three class are-

a)-Piezometer- piezometer is used for measuring only positive pressure (gauge pressure). Piezometer is not used for measuring the gas pressure and negative pressure.

b)-U.Tube Manometer- U-tube manometer are used in two forms, simple and differential. U-Tube manometer used to measuring the pressure of manometric liquid. Manometric liquid are that liquids having specific gravity greater than mercury, alcohol, oil and carbon-tetra chloride. U tube manometer is used to find the pressure difference b/w two points. U tube manometer used to measure relatively high pressure and capable to encounter both positive and negative pressures.

c)- Single column manometer- this is the modified types of U-Type manometer. The area of single column manometer is 100 times of tube area. Capable to measure the pressure at a particular point.

2- Mechanical Gauge- Mechanical gauge are also used in various three forms are-

a)-Bourdon's tube- Bourdon tube is used to measure both gauge (+ve) and vacuum (-ve) pressure. Bourdon tube is used for high pressure pressure as well as low pressure.

👉 Low pressure - Tube made by bronze
👉 High pressure - Tube made by nickel steel

b)- Diaphragm gauge- this type of gauge is used to measure relative low pressure only.

c)- Dead weight pressure gauge- dead weight gauge also known as calibration gauge. This type of gauge most accurate gauge and used for calibration of all other gauges in the laboratory.

📝CHAPTER-4: FLOW & HYDRAULIC ENERGY

In this chapter, I'll discuss about the various six types of flow this is light description about the flow for the purpose of uksssc je exam.

● Steady flow- If the fluid flowing in such a manner the velocity, density and pressure is not change at any point in a cross section area, called steady flow.

●Unsteady flow- If the velocity, density and pressure is different or not same at any point in a cross sectional area, called unsteady flow.

● Uniform flow- if the fluid flowing in such a manner that the rate of change of velocity per unit time is constant, called uniform flow.

● Non-Uniform Flow- if the rate of change of velocity per unit time is not same, called non uniform flow.

● Laminar or stream line flow- If the fluid flowing in a manner the the flow particles not cross the path of each other and follow a linear path, called laminar or stream line flow.

● Turbulent or zig zag flow- if the flowing particles are not flowing in a systematic order and cross each other called Turbulent or zig zag flow.

◆ Discharge (Q)- discharge is the product of area and velocity.

Q = A×V , unit - m^3/sec

◆ Continuity Equation- what flows into a defined volume in a defined time, minus what flows out of that volume in that time, must accumulate in that volume. Also know as mass conservation equation.  A1V1 = A2V2 (incompressible fluid)

For compressible fluid- p¡A1V1=p¡¡A2V2

◆ Hydraulic Energy- the enegry converted through water into mechanical energy and act as more powerful response. Total three type of energy produced by hydro are-

I)- Potential Energy - this energy produced by the self position of fluid and denoted by (z)

II)- Kinematic Energy- this energy produced by the motion or velocity of fluid and denoted by v²/2g

III)- Pressure Energy- this energy produced by the hydraulic head or pressure and denoted by p/w.

Therefore Total Energy = z + v²/2g + p/w

◆ Bernoulli's Theorem- In an Ideal Incompressible fluid when the flow is steady and continuous, the total energy of a flowing particle remain constant at any point.

z + v²/2g + p/w = constant

👉 Each term in Bernoulli's equation represent energy per unit weight.

◆ Applications of Bernoulli's equation-

A- Venturimeter- use to measuring rate of flow of liquid or discharge through pipe. The Venturimeter effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of a pipe. The Venturimeter effect is named after its discoverer, the 18th century Italian physicist, Giovanni Battista Venturi. It consist of three parts, a- converging b)- Throat c)- Diverging

Vanturimetes are available in three forms-

1- Horizontal Venturimeter
2- Vertical Venturimeter
3- Inclined Venturimeter

Q= Cd A¡A¡¡√(2gh)/ √(A¡²-A¡¡²)

👉 Venturimeter dia ratio -1/3 to 1/2

👉 Falling constant of vanturimeter= 0.96 to 0.98

👉Due to variation of Cd (vanturimeter coefficient), not accurate for measuring low velocity discharge.

B- Orifice Platemeter- a simple device used to measuring the discharge in pipe. It works on the same principle as that of venturimeter. It consista of a plate having a sharp edged circular hole known as an orifice. This plate is fixed inside a pipe.The plate thickness is less than or equal to 0.05 times of the pipe dia. The orifice diameter varies from 0.2d to 0.85d, where d is equal to pipe diameter. General kept in 0.5d.

Q= CA¡A¡¡√(2gh)/ √(A¡²-A¡¡²)

👉 Energy losses is less in venturimeter as compare to orifice plate meter.

◆ Velocity of flow measurements- flow measurement is done by following three methods are-

I)- Pitot Tube
II)- Current meter
III)- float

1-Pitot Tube-A pitot tube, also known as pitot probe, is a flow measurement device used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri Pitot in the early 18th century and was modified to its modern form in the mid-19th century by French scientist Henry Darcy. A Pitot tube measures total pressure and static pressure to determine the velocity pressure from which air velocity can be derived.pressure h = v²/2g

2- Current meter- it is used to measuring the velocity of flowing fluid.it consists a wheel or revolving element containing blades or cups, and a tail on which flat vanes are fixed. According to shape of rotating element, current meter are classifieds into-

A- Cup type
B- Propeller type

Cup type current meter

Current meter wheel depth range 0.2 to 0.8m and generally adopted 0.6m.

3- Floats- a floats is a small object made of wood or other suitable material which is lighter than water and thus capable of floating on the water surface. In provides a simple way of measuring the velocity of flow of water in rivers and channels.

📝CHAPTER-5: NOTCH & WEIR

Both are used to measuring discharge. Weir also a notch but used to measuring large discharge. Notch used to measuring greater discharge as compared to orifice. The bottom edge of a notch over which the liquid flow called sill and a sheet of water flowing over a weir called crest. Note the following points here please. 

👉 Correct increasing order of measuring discharge amount is- weir > notch >orifice

👉 notch is generally meant to measure the flow of water from a tank.

◆Notch- Notch is a metallic plate which is used to calculate the small discharge. Notch divided into following categories are-

A- Rectangular Notch

B- Triangular or V-shape Notch

C- Trapezoidal Notch

D- Stepped Notch

V-Notch use to measuring both low or high discharge. Trapezoidal and stepped notch discharge fined by the using same discharge formula v²/2g

♂ Rectangular Notch Discharge-

Q= 2/3 Cd×L×√2g×H^3/2

Q ∝ H^3/2

Error in R/A Notch= 3dh/2h

♂ Triangular Notch Discharge- 

Q= 8/15 Cd×√2g×tan¢/2×H^5/3

Q ∝ H^5/2

Error in V- Notch= 5dh/2h

♂ Trapezoidal or Stepped Notch Discharge-

Q= 2/3 Cd×L×√2g×H^3/2 + 8/15 Cd×√2g×tan¢/2×H^5/3

◆Weir-weir is made by masonry or concrete masonary. Calculate large discharge. Cippoletti weir is a trapezoidal weir with no end contraction. each side of cippoletti weir makes an angle 14°2' with vertical side. Cippoletti weir & Trapezoidal weir having side slope is 1:4 .Weir also defined as following categories are- 

♂ Sharp-crested weir. 

Q= same a rectangular notch

b< H/2

♂ Broad- crested weir. 

Qmax = 1.705Cd×L×H^3/2

b>H/2

♂ Narrow-crested weir. 

Q= same as rectangular notch

b<H/2

♂ Ogee-shaped weir.

Q = same as rectangular notch

b< H/2

b = width of weir

H = height of water above the crest of weir

◆Banzin formula for discharge-

Q= m×L×√2g×H^3/2

m = 0.405+ 0.003/H

◆Franci's formula for discharge-

Q = 1.84 ×(L-0.1nH)×H^3/2

📝CHAPTER-6: FLOW THROUGH PIPE

◆ Closed Conduit:- Closed conduit means any closed natural or artificial duct, such as a pipe, for conveying fluids. It is depends on-

♀ Dia of pipe

♀ Density of fluid

♀ Viscosity

♀ Velocity

◆ Reynold's Number:- Dimensionless quantity

 Re= Inertial force / viscous force

 

Re<2000 - laminar flow

Re>4000 - Turbulent flow

Re- 2000 to 4000 - Transition flow

◆Chezy formula- v=c√(mi)

👉 Need to find the Banzin's formula for chezy constant.

👉 Need to find kutter's formula for chezy constant.

👉 Manning's formula for chezy constant.