Fluid Dynamics
Floating

An object floats on a fluid if its density is less
than that of the fluid
When floating FB = FW
ρfVdispg = ρoVog

ρfVdisp = ρoVo



Fraction of an object submerged is given by
the ratio of the density of the object to the
fluid
Example

A rectangular block of wood (1.0m x
2.0m x 0.25m) floats so that 0.15 cm of
its height is above the water level.
a) find the density of the wood
b) find the mass of the wood
Example

A continental block (ρ = 2800 kg/m3)
floats on the mantle (ρ = 3300 kg/m3).
Assuming the continent is 35km thick,
estimate the height of the continent
floating above the mantle
Fluid Dynamics


Describes motion of fluids
Two types of fluid flow
- streamline or laminar flow – smooth
- turbulent flow – erratic small circles
Streamline or Laminar Flow
Turbulent Flow
Flow Rate


Mass of a fluid that passes a given point
per unit of time
Equation of continuity
A1v1 = A2v2
Example

Water flows through a pipe of diameter
of 3.0 cm at a flow speed of 6.0 m/s.
The pipe expands to a diameter of 9.0
cm, what is the new flow speed?
Example

The radius of the aorta is about 1.0cm
and the blood passing through it has a
speed of about 30cm/s. A typical
capillary has a radius of about 4 x10-4
cm, and blood flows through it at a
speed of about 5 x 10-4m/s. Estimate
the number of capillaries in the body.
Bernoulli’s Principle

Where the velocity of a fluid is high, the
pressure is low, and where the velocity
is low, the pressure is high
Bernoulli’s Equation
P1 + ½ρv12 + ρgy1 = P2 + ½ρv22 + ρgy2
Example

Water circulates throughout a house in
a hot-water heating system. If the
water is pumped at a speed of 0.50m/s
through a 4.0cm diameter pipe in the
basement under a pressure of 300 kPa,
what will the flow speed and pressure
be in a 2.6cm diameter pipe on the
second floor 5.0m above?
Applications
A large tank, 25m in height and
open at the tope is completely
filled with water. An opening
5m from the bottom allows
water to flow out. What
velocity will the water leave
the tank?