4) Fluid,flows and Viscosity

Question 1

Viscosity

Answer 1

The adjacent layers of a flowing fluid interacts with forces parallel to the surface of the layers. They experience internal friction

Viscosity is the property of a fluid that characterises the magnitude of the internal friction

Question 2

Newton’s law of viscosity

Answer 2

F=-n dv/dx s

n= dynamic viscosity coefficient

N depends on the molecular property of the fluid and on temperature

Question 3

Newtonian and non-Newtonian fluids

Answer 3

Fluids that obey Newton’s law of viscosity are called Newtonian

The viscosity coefficient of some fluids depends on the velocity gradient
- these fluids are not described by the Newton’s law and are called non-Newtonian fluids

Question 4

Non Newtonian fluids

Answer 4

Fluids with large complex molecules are often non Newtonian and have high viscosity

The viscosity of blood at the centre line and close to the walls of blood vessels is different as blood cells move mainly at the centre

Blood is a non Newtonian fluid

Question 5

Hematocrit

Answer 5

Hematocrit- the ratio of the volume of the suspended particles to the total volume of the suspension
Blood is a suspensions of blood cells in blood plasma

Hematocrit of blood is 40-60%
Blood viscosity depends on the viscosity or the blood plasma and hematocrit

Question 6

Viscous fluid flow in a cylindrical tube

Answer 6

The velocity of a fluid in a tube depends on the distance from the tube wall

Fluid velocity is maximum at the centre line of the tube

Blood vessels are cylindrical tubes

Question 7

The law of poiseuille

Answer 7

Q=pi/8n x R^4/L x (p_1 - p_2)

Q= flow rate-the volume of fluid per unit of time flowing through a cross section of the tube
n= fluid viscosity
R= tube radius
L= tube length
P1 and p2 fluid pressure at the input and output of the tube

DRAWING

Question 8

Hydraulic resistance of a tube

Answer 8

X=8n/pi L/R^4

X depends on tube dimension and fluid viscosity

Law of Poiseuille = p1-p2/ X

Question 9

Movement of body in viscous fluid

Answer 9

A body moving in a viscous fluid experiences a force opposite to the direction of its velocity - a drag force

Drag force depends on :
Fluid of viscosity 
Body size 
Shape 
Velocity

Question 10

Stoke’s law

Answer 10

Drag force F_d on a spherical body moving in a viscous fluid 
F_d=6pi nrv
n=fluid viscosity
r= radius 
v= velocity relative to the fluid 

Law holds for slow, uniform rectilinear motion far away from other bodies or walls

DRAWING

Question 11

Laminate and turbulent flows

Answer 11

Laminate or streamlined
-when fluid flows in layers

In laminar layers the fluids don’t mix

Turbulent or edgy flows
-when fluid molecules move along crossing lines and the fluid layers mix

Question 12

Reynolds number

Answer 12

This is a dimensionless quantity that characterises the type of flow
Laminar or turbulent

Re= pvD/n

P=fluid density
V=fluid velocity
N=fluid viscosity
D=characteristic dimension eg diameter

Question 13

Transition between laminar and turbulent

Answer 13

Re<1000 then laminar

10002000 flow is turbulent

Critical values of Re are approximations are depends on many characteristics of the flow

Question 14

Blood flow

Answer 14

The normal blood flow is

• turbulent in the aorta and through heart valves
• laminar in other blood vessels

In some arteries the re number is close to the critical value. Turbulence may appear if blood viscosity or the diameter of the artery are decreased

Question 15

Turbulent blood flow

Answer 15

A turbulent flood flow requires additional energy to maintain the same flow rate as laminar due to ^ internal friction resulting in energy loss

The work done by the ❤️ increases when abnormal turbulence of blood flow appears

The noise generated by the turbulent blood can be used for diagnostic purposes
Eg : blood pressure

Question 16

Turbulent air flow

Answer 16

The normal air in airways in laminar

Some diseases may cause air flow to become turbulent

The inspiration muscles have to deliver more power when the air flow is turbulent

Question 17

Viscosity measurement

Answer 17

Viscometry= method used to measure viscosity 
Viscometer= instrument used to measure viscosity 

Method for viscosity measurements are based on:
Newton’s law of viscosity
Poiseuilles law
Stokes law

Question 18

Viscosity measurement using stokes law

Answer 18

Forces which act on a sphere experiencing a free fall in the investigated fluid

Gravity:
G=pVg
Buoyant force:
F_a= P_0Vg
Drag:
F_d=6pi nrv

Question 19

Viscosity measuring stokes law 2

Answer 19

The sphere reaches terminal velocity v when
G=F_a + F_d

If r, p and p0 are known and v is measured then n can be calculated

n= 2g/g p-p0/v r^2

Question 20

Erythrocytes sedimentation rate

Answer 20

The sedimentation of erythrocytes in blood plasma can be modelled by free falling spheres in viscous fluid

It is measured in mm/h