Density and viscocity
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This document discusses different methods of measuring density and viscosity. It describes three main types of densitometers - displacement, fluid dynamic, and capacitance types. Displacement densitometers use a float that rises or falls based on the density of the fluid. Fluid dynamic densitometers measure differential pressure. Capacitance densitometers measure the capacitance between concentric cylinders separated by the fluid. Viscosity is also defined, and three common viscometers are described - capillary tube, falling ball, and rotating concentric cylinder viscometers. Capillary tube viscometers time fluid flow through a tube, falling ball viscometers time a ball's descent, and rotating viscometers measure torque on a
![9AEI405.19 TO 20 54
In equilibrium condition the upward forces are equal to
downward forces
Fl + F = W
F = W – Fl
6πμrv = 4/3 π3ρb g – 4/3 π r3ρl g
= 4/3 πr3g (ρb – ρl)
μ = [4/3 π r3g (ρb – ρl)] / 6rv
=[2/9 r2g(ρb – ρl)] /V](https://image.slidesharecdn.com/densityandviscocity-170225020239/85/Density-and-viscocity-54-320.jpg)
![9AEI405.21 59
• If the annular space (r2 – r1) is sufficiently small in
comparison to the radius of the inner cylinder, then a
torque produced on vertical side of the inner cylinder
• The relation between coefficient viscosity and torque is
given by
μ = [T1(r2 – r1)] /(2πwr1
2
r2L)
T1 = [µ2πwr1
2
r2L] ÷ (r2 – r1)](https://image.slidesharecdn.com/densityandviscocity-170225020239/85/Density-and-viscocity-59-320.jpg)
Density and viscocity
- 2. 9AEI405.22 2 • It is defined as the mass (m) per unit volume (v) . ρ = m/v The unit of density is kg/m3 Definition
- 3. 9AEI405.22 3 Fig 1 •Volume is measured with a graduated jar •Mass is measured with weighing machine •By knowing volume and mass density can be measured
- 4. 9AEI405.22 4 Necessity of measurement of density • Density measurement is necessary in chemical industries where the determination of concentration of a solution or mixture is based on density. • In flow measurements while converting the volumetric flow rate into the mass flow rate, the density of a substance should be known.
- 5. 9AEI405.22 5 Types of densitometers • Densitometer is a device used to measure the density of a given sample • There are three types of densitometers • They are : • Displacement type densitometers • Fluid dynamic type densitometers • Capacitance type densitometers
- 7. 9AEI405.23 7 Operation • It mainly consists of float and chain • The test liquid will flow through the transparent chamber from bottom to top. • When the density of the fluid increases a buoyant force increases in the test liquid. • The increase in the force would cause the flow to rise.
- 8. 9AEI405.23 8 Displacement type densitometer Fig 1
- 9. 9AEI405.23 9 • As the float rises it will take up a greater portion of the chain. • When the density of test liquid decreases the float comes down. • A greater portion of the chain weight is taken up by the supports. Operation
- 10. 9AEI405.23 10 • The float moves according to the density of the test fluid. • The position of the float can be seen through transparent chamber in which the measurement is carried out. • The new float position is a function of the density. Operation
- 12. 9AEI405.24 Fluid dynamic type densitometer Supply of nitrogen with known density Sample outlet Supply nozzle (nr) Receiver (rr) Fig 1
- 13. 9AEI405.24 Operation • It is used to measure the densities of gases and liquids. • It mainly consists of two chambers • Reference chamber • Measuring chamber
- 14. 9AEI405.24 Reference chamber: • The reference chamber consists of • Supply nozzle (Nr) • Receiver port (Rr) • A small outlet port
- 15. 9AEI405.24 • This chamber is filled with suitable supply of nitrogen at known density such that the reference pressure (Pr) serves as a reference value at the receiver port.
- 16. 9AEI405.24 Measuring Chamber • The measuring chamber consists of • Inlet • Outlet • Supply Nozzle (Nm) • Receiver port (Rm) • This chamber is placed into directly adjacent to reference chamber
- 17. 9AEI405.24 • The measuring fluid or gas is pumped through the inlet and this chamber also receives the nitrogen with known density • The differential pressure between the receiving port and measuring port is a measure of the density of unknown sample
- 19. 9AEI405.25 Capacitance type densitometer INNER ELETRODE OUTER ELETRODE A.C . EXITATION HOLES FOR FLUID ENTRY AND EXIT Fig 1
- 20. 9AEI405.25 • It mainly consists of two concentric cylinders • The sample whose density is to be measured is placed between these two cylinders • These cylinders acts as two parallel plates of a capacitor and the sample acts as the dielectric between the plates Capacitance type densitometer
- 21. 9AEI405.25 • The two cylinders are connected to one arm of a bridge circuit and the outer cylinder consists of holes for fluid entry and exit • The bridge circuit measures the capacitance between the two cylinders • The capacitance is proportional to dielectric constant which is in turn is proportional to the density of the fluid
- 23. 9AEI405.16 Introduction • It is a measure of the fluidity of the liquid or the gas • Many fluids undergo continuous deformation with the application of shearing stress • This shear force produces a flow • If the force-flow relation is linear then the fluid is said to be Newtonian
- 24. 9AEI405.16 • For non Newtonian fluids the relation is not only non- linear but changes from material to material • When continuous deformation occurs the fluid tries to oppose this with frictional resistance • This resistance is measured in terms of consistency
- 25. 9AEI405.16 Fig.1
- 26. 9AEI405.16 Definition: • Consistency of Newtonian fluids is called” Viscosity” ( / ) S dv dz µ = • It is often formulated as the ratio of shear stress to shear rate
- 27. 9AEI405.16 Fig 3
- 28. 9AEI405.16 Where • S is the shear stress • dv/dz is the velocity gradient The unit of viscosity is Newton-Sec/m2 = 10 poise Fluidity is the reciprocal of viscosity units are rhe = 1/poise
- 29. 9AEI405.16 ( )υKinemetic viscosity /υ µ ρ= • It is the ratio of absolute viscosity to density of the fluid in cm2/sec, or stokes Specific viscosity /s stµ µ µ= • It is the ratio of absolute viscosity of the fluid to the absolute viscosity of the standard fluid at the same temperature.
- 30. 9AEI405.16 • It is the ratio of the absolute viscosity of the fluid at a given temperature to the absolute viscosity of a standard fluid at 200 c. • Viscosity index (Iv) • It is an emperical number that indicates the effect of changes of temperature on viscosity of the fluid ( )RµRelative viscosity
- 31. 9AEI405.16 Fig 4
- 32. 9AEI405.16 Necessity: • Measurement of viscosity of lubricating oils, fuels, paints is taken into consideration before their use Lubricating oils :- • Lubricating should be sufficiently viscous so that they are not squeezed out from the bearings • Further they should not be too viscous to increase the resistance to the motion between the moving parts.
- 33. 9AEI405.16 Paints :- • In paint spraying the viscosity of paint should be maintained with certain limits • Hence the measurement of viscosity is necessary in process industries
- 34. 9AEI405.16 Types of viscometer • There are mainly three types of viscometers used in measurement viscosity. • They are: • Capillary tube viscometer • Falling ball viscometer • Rotating concentric cylinder viscometer
- 35. Capillary Tube Viscometer 9AEI405.17 TO 18 35
- 36. 9AEI405.17 TO 18 36 Capillary Tube Viscometer Flow in Constant head (h) Liquid vessel Flow Capillary tube Measuring jar Overflow Liquid Flow in Constant head (h) Liquid vessel Flow Capillary tube Measuring jar Overflow Liquid L Fig1
- 37. 9AEI405.17 TO 18 37 Capillary Tube Viscometer • It mainly consists of a • Liquid vessel • Capillary tube • Measuring jar • The measuring jar is used to collect the specified volume of sample liquid • The constant pressure head or hydrostatic head of fluid causes the liquid flow through the capillary tube Flow in Constant head (h) Liquid vessel Flow Capillary tube Measuring jar Overflow Liquid Flow in Constant head (h) Liquid vessel Flow Capillary tube Measuring jar Overflow Liquid L
- 38. 9AEI405.17 TO 18 38 • The discharge rate (Q) can be easily calculated by using measuring jar and stop watch Volume of liquid collected in the measuring jar Time taken to collect the liquid in the measuring jar Q =
- 39. 9AEI405.17 TO 18 39 If the flow is laminar, the discharge rate (Q) is given by Where Q = Volume of the liquid passing through the tube per second L = Length of the capillary tube D = Diameter of the capillary tube μ = Coefficient of viscosity ΔP = pressure drop across the ends of the tube Q = πD4ΔP 128μL
- 40. 9AEI405.17 TO 18 40 ΔP = ρ g h Where ρ = Density of the fluid g = Acceleration due to gravity h = constant head Q = πD4ρg h 128μL μ = πD4 ρg h 128QL
- 41. 9AEI405.17 TO 18 41 • In the above equation the diameter of Capillary tube is raised to fourth power • Hence it is essential to measure it as accurately as possible • By using traveling microscope the diameter of the capillary tube can be measured accurately • Capillary tube viscometer can be used as a flow metering device if the viscosity of the liquid is known
- 42. 9AEI405.17 TO 18 42 Advantages • Simple in construction • No maintenance required • Easy to use
- 43. 9AEI405.17 TO 18 43 Disadvantage • The main disadvantage of this viscometer is that it is not suitable for unclean fluids as the dirt or grit tends to clog the capillary tube
- 44. 9AEI405.17 TO 18 44 Applications • They can be used as secondary standards for the calibration of other type of viscometers • They are used in the refineries to measure the viscosity of petroleum products
- 45. Falling Ball Viscometer 9AEI405.19 TO 20 45
- 46. 9AEI405.19 TO 20 46 Falling ball Viscometer • Falling ball Viscometer is a device used to calculate the coefficient of viscosity (µ) of a given sample
- 47. 9AEI405.19 TO 20 47 1. Cap 2. Capillary tube 3. Steel ball 4. Liquid whose viscosity is to be measured 5. Base 6. Marking denoting falling ball distance to be timed Falling Ball Viscometer Fig 1
- 48. 9AEI405.19 TO 20 48 Falling ball viscometer-Principle of operation • It consists of essentially a precision glass tube of 200 mm length • A perfectly smooth steel ball freely released from the rest into the test liquid under gravitational force • The ball obtains a maximum terminal velocity, when upward and downward forces acting on it which are equal
- 49. 9AEI405.19 TO 20 49 • The following forces act on the ball • Weight of ball (w) • Upward force (fl) • Viscous force (F)
- 50. 9AEI405.19 TO 20 50 Fig 2
- 51. 9AEI405.19 TO 20 51 • Weight of the ball that acts vertically downward i.e. w = 4/3 π r3 ρb g • Where r = Radius of ball ρb = Density of ball g = Acceleration due to gravity
- 52. 9AEI405.19 TO 20 52 Upward force (fl) of the fluid due to buoyancy i.e. Fl = 4/3 π r3ρlg Where ρl = Density of the liquid whose viscosity is to be measured
- 53. 9AEI405.19 TO 20 53 Viscous force (F) in upward direction i.e. F = 6πμr v Where μ = Coefficient of viscosity V = Constant velocity with which the ball moves through the liquid
- 54. 9AEI405.19 TO 20 54 In equilibrium condition the upward forces are equal to downward forces Fl + F = W F = W – Fl 6πμrv = 4/3 π3ρb g – 4/3 π r3ρl g = 4/3 πr3g (ρb – ρl) μ = [4/3 π r3g (ρb – ρl)] / 6rv =[2/9 r2g(ρb – ρl)] /V
- 55. 9AEI405.19 TO 20 55 • The terminal velocity (V) can be calculated by measuring the timing of the fall of the ball and the distance between the markings on the glass tube • V= Distance / Time • By measuring the density of ball (ρb), density of liquid (ρl), radius of the ball (r) and knowing terminal velocity (V) the coefficient of viscosity (µ) can be calculated
- 57. 9AEI405.21 57 Rotating concentric cylinder viscometer 1. Fixed end torsion wire 2. Rotating cylinder 3. Stationary cylinder 4. Liquid under test Fig 1
- 58. 9AEI405.21 58 • It consists of two concentric cylinders, inner cylinder and outer cylinder • The outer cylinder is rotated at a constant angular speed and the inner cylinder is stationary • A small annular space contains the fluid whose viscosity is to be measured • The viscous drag due to the fluid between the cylinders produce a torque on the inner cylinder Rotating Concentric Cylinder Type Viscometer
- 59. 9AEI405.21 59 • If the annular space (r2 – r1) is sufficiently small in comparison to the radius of the inner cylinder, then a torque produced on vertical side of the inner cylinder • The relation between coefficient viscosity and torque is given by μ = [T1(r2 – r1)] /(2πwr1 2 r2L) T1 = [µ2πwr1 2 r2L] ÷ (r2 – r1)
- 60. 9AEI405.21 60 • When the annular space ‘a’ is very small then additional viscous drag torque is produced on the inner cylinder due to bottom disk • The relationship between coefficient of viscosity and the torque is given by µ = (2T2a) ÷ (Π wr1 4 ) T2 = (μπwr1 4 ) ÷ 2a
- 61. 9AEI405.21 61 • The total torque produced on inner cylinder is T = T1 + T2 μ2πwr12r24 + μπwr14 = (r2 – r1) 2a = μπwr12 2r2L + r12 (r2 – r1) 2a
- 62. 9AEI405.21 62 • The coefficient of viscosity πr12w 2r2L r2 – r1 + r12 2a T μ =