Transcript Applicatiosn of Moving fluids: Water hoses, Balls & Frisbees

The Physics of Balloons
and Submarines…cont’d…
The Ideal Gas Law Equation
We learned that Pressure of an Ideal Gas is proportional to Particle Density.
P
Temperature is a measure of the average kinetic energy of atoms, and
is related to the pressure. In fact, Pressure is proportional to Temperature.
PT
This leads to the ‘ideal gas law equation’
(holds only for non-interacting particles):
P=kT
Boltzmann’s constant
1.38 x 10-23 Pa-m3/particle-K
Particle density
Absolute Temperature ( Kelvin)
C + 273 =  K(Kelvin scale)
e.g. 0 C = 273  K
Do fluids obey Newton’s Laws ?
Consider a horizontal pipe with some fluid:
P1
P2
1. Fluids have inertia (need to apply forces to change their flow. )
2. Pressure differences P1-P2 lead to net force, acceleration to the right.
Fluids accelerate to lower pressures. (similar to F=ma)
3. Apply pressure on fluid; fluid applies same amount of pressure on you
(Newton’s 3rd law)
• Pumping water requires work.
• Pumped water carries this energy with it.
• For Steady State flow, Work done in moving volume V using Pressure P
= P  V (similar to F  d)
= ‘energy required to pump fluid’ for steady state flow
‘Pressure potential energy’
For horizontal flow:
Total Energy E of Fluid = PV + Kinetic Energy
Energy/unit volume E/V = P + (½)v2 = constant,
(for horizontal flow)
In general (including vertical flow):
P + (½)v2 + gh = constant (along a streamline)
i.e. When a stream of water speeds p in a nozzle or flows uphill
in a pipe, its pressure drops. (Bernoulli’s Principle/Equation)
A: slow velocity,
high Pressure
Examples:
A
B
A
B: fast velocity,
low Pressure
The Perfume Atomizer
Airplane Wing
Why does the ball float ?
Physics of Moving Fluids:
In Garden Hoses, around Baseballs, Planes and Frisbees
Fluids in Motion: Using Hoses, Baseballs & Frisbees
Real liquids have viscosity – fluid friction when 1 layer of fluid
tries sliding across another.
e.g.
Fluid
Viscosity
Honey (20C)
1000 Pa-s
Water (20C)
0.001 Pa-s
Helium (2C)
0 Pa-s
Result: Speed of H20 thru a pipe is not constant (fastest at the
center, stationary at the walls)
Velocity profile due to viscosity
Viscosity affects the volume flow rate through a hose or pipe.
p1
p2
In fact:
length L
Volume flow rate V/t =   p 
128  L  
(Poiseuille’s Law)
D4
Diameter D
p = p1 - p2
viscosity
Or….It’s hard to squeeze honey thru a long, thin tube.
Example:
When new, a kitchen faucet delivered 0.5 liters/s. Mineral deposit
built up, reducing diameter by 20 % over the years. What’s the new
volume flow rate ?
Since V/ t  D4, and D is now 0.8 of its value before,
then V/ t changed by a factor of (0.8)4, or it is currently 0.2 liter/s.
( a reduction of  60 % !).
How Frisbees Fly
Above Frisbee:
• airflow bends inward
• high velocity
• lower pressure
Below Frisbee:
• airflow bends outward
• low velocity
• higher pressure
Pressure Difference gives ‘lift’
A Spinning Baseball
Magnus Force
Low Pressure
Spin
High Pressure
Direction of throw
• Spin forces flow on one side to be faster,
resulting in lower pressure.
• Spin forces flow on the other side to be slower,
resulting in higher pressure.
• Pressure difference causes a lateral deflection
Laminar vs Turbulent Flow
• Flow near surface forms a ‘boundary layer’
• If Reynolds number < 100,000
• laminar flow of boundary layer
• slowed by viscous drag
• If Reynolds number > 100, 000
• Turbulent flow of boundary layer
Reynolds number = density  obstacle length  flow speed
viscosity