Physics in Life Sciences
Fluid
flow in
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: the
velocity of fluid particles
at any point of the fluid
changes as time passes.
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
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.
Mass flow rate m

 1 A1v1
at position 1
t
Mass flow rate
  2 A2 v2
at position 2
 2 A2 v2  1 A1v1
A1v1
v1 
( 1   2 )
A2
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 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.
In the carotid artery in the neck, blood flows three times faster
through a partially blocked region than it does through an
unobstructed region.
5MHz
Doppler flow meter to
measure the speed of red
blood cells.
To locate regions where
blood vessels have
narrowed.
A1v1 = A2v2, (1 = 2)

r v

2
U
U
Unobstructed
Volume flow rate


r v

2
O
O
Obstructed
Volume flow rate
The ratio of the radii is
rU
vO

 3  1.7
rO
vU
A2 , v2
 2 A2 v2  1 A1v1
A2 v2
v1 
( 1   2 )
A1
A1 ,v1
Circulation
Honey drop (viscous flow)
Pipe
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.
Why do we have viscosity?
Internal
resistance
It is due to
Internal
resistance
Lamellar flow
With friction or air resistance PE
KEPE+Heat
Stop here
A roller
coaster track
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).
Laminar flow
The viscosity of a fluid is described by the coefficient of
viscosity 
SI Unit of Viscosity: Pa · s
The viscosity  of the fluid
Due to the viscosity, P2 > P1
Air resistance
v = 30m/hr
F
Friction
In order to maintain a constant
velocity, a force F should be applied.
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
 8L 
Q 4   P2  P1 
 R 
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