Physics 1501: Lecture 33 Today ’ s Agenda. Homework #11 (due Friday Dec. 2) Midterm 2: graded by Dec. 2 Topics: Fluid dynamics Bernouilli ’ s equation Example of applications. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Warning: the explanations in text books are generally over-simplified!
Curve ball (baseball), slice or topspin (golf) ball drags air around (viscosity) air speed near ball fast at “top” (left side) lower pressure force sideways acceleration or lift
The tank is open to the atmosphere atthe top. Find and expression for the speed of the liquid leaving the pipe atthe bottom.
Example: Efflux SpeedExample: Efflux Speed
Physics 1501: Lecture 33, Pg 12
SolutionSolution
Physics 1501: Lecture 33, Pg 13
vh
y
A
B
C
O
A siphon is used to drain water from a tank (beside). The siphon has a uniform diameter. Assume steady flow without friction, and h=1.00 m. You want to find the speed v of the outflow at the end of the siphon, and the maximum possible height y above the water surface.
ExampleExampleFluid dynamicsFluid dynamics
Use the 5 step method Draw a diagram that includes all the relevant quantities for this
problem. What quantities do you need to find v and ymax ?
What concepts and equations will you use to solve this problem? We have fluid in motion: fluid dynamicsFluid is water: incompressible fluidWe therefore use Bernouilli’s equation
Solve for v and ymax in term of symbols. Incompressible fluid: Av =constantA is the same throughout the pipe vA= vB= vC = v To get ymax , use the points C and B (could also use A)
where: PB=Patm=1 atm and vB=v and yB=-h
set : PC=0 (cannot be negative) and vC=v and yC= ymax
Verify the units, and verify if your values are plausible. [v] = L/T and [ymax] = L so units are OK
v of a few m/s and ymax of a few meters seem OK
» Not too big, not too small
Note on approximation Same as saying
PA= PO =Patm or vA=0
i.e. neglecting the flow in
the pipe at point A vh
y
A
B
C
O
Physics 1501: Lecture 33, Pg 20
In ideal fluids mechanical energy is conserved (Bernoulli) In real fluids, there is dissipation (or conversion to heat) of
mechanical energy due to viscosity (internal friction of fluid)
Real Fluids: ViscosityReal Fluids: Viscosity
Viscosity measures the force required to shear the fluid:
where F is the force required to move a fluid lamina (thin layer) of area A at the speed v when the fluid is in contact with a stationary surface a perpendicular distance y away.
area A
Physics 1501: Lecture 33, Pg 21
Viscosity arises from particle collisions in the fluid as particles in the top layer
diffuse downward they transfer some of their momentum to lower layers
Real Fluids: ViscosityReal Fluids: Viscosity
Viscosity (Pa-s)
oilair glycerinH2O
area A
lower layers get pulled along (F = p/t)
Physics 1501: Lecture 33, Pg 22
p+p Qr
L
pR
Because friction is involved, we know that mechanical energy is not being conserved - work is being done by the fluid.
Power is dissipated when viscous fluid flows: P = v·F = Q ·p the velocity of the fluid remains constant power goes into heating the fluid: increasing its entropy
Real Fluids: Viscous FlowReal Fluids: Viscous Flow
How fast can viscous fluid flow through a pipe? Poiseuille’s Law
Physics 1501: Lecture 33, Pg 23
1) Given that water is viscous, what is the ratio of the flow rates, Q1/Q1/2, in pipes of these sizes if the pressure drop per meter of pipe is the same in the two cases?
Consider again the 1 inch diameter pipe and the 1/2 inch diameter pipe.