Lecture 9 (1)Lecture 9 (1)

Physics in Life SciencesPhysics in Life Sciences

Fluid flow in human body2

Fluid flow in human body2

Do you know

•You have 80,000km of blood vessels

•B747: Nonstop flight for 100 hrs

Flow: the movement of fluid particles.

At different locations in the stream the particle velocities may be different, as indicated by v1 and v2.

Steady flow : the velocity of fluid particles at any point is constant as time passes.

In steady flow, the pattern of streamlines is steady in time, and no two streamlines cross one another.

Unsteady flow - Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast-moving fluid

Unsteady flow - Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast-moving fluid

Unsteady flow: the velocity of fluid particles at any point of the fluid changes as time passes.

Compressible or incompressible flow

Compressible flow: the density of a fluid varies as the pressure changes

-gases are highly compressible.

Incompressible flow: the density of a fluid remains constant as the pressure changes

- liquids flow in an incompressible manner.

Compressible or incompressible flow

Compressible flow: the density of a fluid varies as the pressure changes

-gases are highly compressible.

Incompressible flow: the density of a fluid remains constant as the pressure changes

- liquids flow in an incompressible manner.

•The mass of fluid per second (e.g., 5 kg/s) that flows through a tube is called the mass flow rate.

•Conservation of mass flow: If a fluid enters one end of a pipe at a certain rate (e.g., 5 kilograms per second), then fluid must also leave at the same rate, assuming that there are no places between the entry and exit points to add or remove fluid.

•The mass of fluid per second (e.g., 5 kg/s) that flows through a tube is called the mass flow rate.

•Conservation of mass flow: If a fluid enters one end of a pipe at a certain rate (e.g., 5 kilograms per second), then fluid must also leave at the same rate, assuming that there are no places between the entry and exit points to add or remove fluid.

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rate flow Mass

1position at

rate flow Mass

vA

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A

vAv

vAvA

EQUATION OF CONTINUITY

The mass flow rate (Av) has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. For two positions along such a tube

1A1v1 = 2A2v2

= fluid density (kg/m3)

A = cross-sectional area of tube (m2)

v = fluid speed (m/s)

SI Unit of Mass Flow Rate: kg/s

EQUATION OF CONTINUITY

The mass flow rate (Av) has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. For two positions along such a tube

1A1v1 = 2A2v2

= fluid density (kg/m3)

A = cross-sectional area of tube (m2)

v = fluid speed (m/s)

SI Unit of Mass Flow Rate: kg/s

1A1v1 = iAivi

Cholesterol and Plugged ArteriesCholesterol and Plugged Arteries

A clogged artery

In the condition known as atherosclerosis, a deposit or atheroma forms on the arterial wall and reduces the opening through which blood can flow.

Doppler flow meter to measure the speed of red blood cells.

To locate regions where blood vessels have narrowed.

5MHz

In the carotid artery in the neck, blood flows three times faster through a partially blocked region than it does through an unobstructed region.

In the carotid artery in the neck, blood flows three times faster through a partially blocked region than it does through an unobstructed region.

                               

The ratio of the radii is

                       

A1v1 = A2v2, (1 = 2)

rate flow Volume

Obstructed

2

rate flow VolumeedUnobstruct

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Circulation

Honey drop (viscous flow)

1. Water drop - nonviscous flow-all fluid particles across the pipe have the same velocity

2. Honey (or blood) drop-A viscous - does not flow readily-different layers have different velocity.

1. Water drop - nonviscous flow-all fluid particles across the pipe have the same velocity

2. Honey (or blood) drop-A viscous - does not flow readily-different layers have different velocity.

Pipe

Lamellar flow

Why do we have viscosity?

Internal resistance

It is due to Internal

resistance

With friction or air resistance

A roller coaster track

PE KEPE+Heat

Stop here

Energy form A Energy form B + thermal energy

•The flow of a viscous fluid (blood, honey) is an energy-dissipating process. The viscosity hinders neighboring layers of fluid from sliding freely past one another.

•A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. •An incompressible, nonviscous fluid is called an ideal fluid (water).

•The flow of a viscous fluid (blood, honey) is an energy-dissipating process. The viscosity hinders neighboring layers of fluid from sliding freely past one another.

•A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. •An incompressible, nonviscous fluid is called an ideal fluid (water).

The viscosity of a fluid is described by the coefficient of viscosity

SI Unit of Viscosity: Pa · s

Laminar flow

The viscosity   of the fluid

Due to the viscosity, P2 > P1

In order to maintain a constant velocity, a force F should be applied.

v = 30m/hr

FrictionF

Air resistance

The volume flow rate Q (in m3/s) of the viscous fluid:•a difference in pressures P2 - P1 must be maintained between any two locations along the pipe in order for the fluid to flow. And Q ~ P2 - P1

•a long pipe offers greater resistance to the flow than a short pipe does- Q is inversely proportional to the length L.

•Q is inversely proportional to the viscosity .

•Q being proportional to the fourth power of the radius, or R4.

The volume flow rate Q (in m3/s) of the viscous fluid:•a difference in pressures P2 - P1 must be maintained between any two locations along the pipe in order for the fluid to flow. And Q ~ P2 - P1

•a long pipe offers greater resistance to the flow than a short pipe does- Q is inversely proportional to the length L.

•Q is inversely proportional to the viscosity .

•Q being proportional to the fourth power of the radius, or R4.

the viscosity   of the fluid

POISEUILLE'S LAW

A fluid whose viscosity is , flowing through a pipe of radius R and length L, has a volume flow rate Q given by

POISEUILLE'S LAW

A fluid whose viscosity is , flowing through a pipe of radius R and length L, has a volume flow rate Q given by

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Graph of blood pressure vs time in a major artery

• Viscous and non-viscous flow

• Physics of viscosity

• POISEUILLE'S LAW

•Blood pressure and circulation