Classical Mechanics
Lecture 26
Today’s Concepts:
A) Moving Fluids
B) Bernoulli’s Equation
Mechanics Lecture 26, Slide 1
Clicker Question
This picture is
A) Real
B) Fake
Mechanics Lecture 26, Slide 2
Clicker Question
Through which hole will the water come out fastest?
A
DP = rgDy
B
C
Mechanics Lecture 26, Slide 3
CheckPoint
Water flows through a pipe that has a constriction in the middle as shown.
How does the speed of the water in the constriction compare to the speed
of the water in the rest of the pipe?
A) It is bigger
B) It is smaller
C) It is the same
Water is incompressible so when it goes through the
constriction the water has to speed up in order to
squeeze all the water through
Mechanics Lecture 26, Slide 4
CheckPoint
Water flows through a pipe that has a constriction in the middle as shown.
How does the pressure of the water in the constriction compare to the
pressure of the water in the rest of the pipe?
A) It is bigger
B) It is smaller
C) It is the same
Mechanics Lecture 26, Slide 5
CheckPoint
Water flows through a pipe that has a constriction in the middle as shown.
How does the pressure of the water in the constriction compare to the
pressure of the water in the rest of the pipe?
A) It is bigger
B) It is smaller
C) It is the same
A) because it's being forced through a smaller pipe it has
greater pressure.
B) Pressure must be the same throughout the pipe.
C) Since the fluid is all at the same height the sum (P +
.5pv²) is constant throughout the pipe. The velocity is
greater in the constriction, so the pressure there must
be smaller.
Mechanics Lecture 26, Slide 6
Clicker Question
Two empty pop cans are placed about ¼” apart on a frictionless surface.
If you blow air between the cans, what happens?
A) The cans move toward each other.
B) The cans move apart.
C) The cans don’t move at all.
Mechanics Lecture 26, Slide 7
CheckPoint
Water flows from left to right along a pipe as shown. The right end
of the pipe is twice as high as and also has four times the area of
the left end. Which of the following statements best relates the
pressures at the ends of the pipe?
A) PL = 2PR
B) PL = PR
C) PL = ½ PR
D) The relative size of PL and PR depends
on the speed of the flow.
hR
hL
0
PR
PL
1
1
PL  rvL2  rghL = PR  rvR2  rghR Bernoulli’s
2
2
Equation
Mechanics Lecture 26, Slide 9
Clicker Question
Suppose the water isn't moving. The right end of the pipe is twice as high as and also has
four times the area of the left end. Which of the following statements best relates the
pressures at the ends of the pipe?
A) PL = 2PR
B) PL = PR
C) PL = ½ PR
D) PL - PR = rg (hr - hL)
hR
hL
0
PR
PL
1
1
PL  r vL2  r ghL = PR  r vR2  r ghR Bernoulli’s
2
2
Equation
Mechanics Lecture 26, Slide 10
Clicker Question
Water flows from left to right along a pipe as shown. The right end of the pipe is
twice as high as and also has four times the area of the left end. Which of the
following statements best relates the pressures at the ends of the pipe?
A) PL = 2PR
B) PL = PR
C) PL = ½ PR
D) PL - PR =rg (hR - hL)  1/2r (vR2 - vL2)
hR
hL
0
PR
PL
1
1
PL  r vL2  r ghL = PR  r vR2  r ghR Bernoulli’s
2
2
Equation
Mechanics Lecture 26, Slide 11
Clicker Question
We just saw that PL - PR can be written in the following way:
(
1
PL - PR = rg (hR - hL ) - r vL2 - vR2
2
)
Is there any reason this has to mean PL = 2PR or PL = PR or PL = ½ PR
A) Yes
B) No
hR
hL
0
PR
PL
1
1
PL  r vL2  r ghL = PR  r vR2  r ghR Bernoulli’s
2
2
Equation
Mechanics Lecture 26, Slide 12
CheckPoint
Water flows from left to right along a pipe as shown. The right end of the pipe is twice as
high as and also has four times the area of the left end. Which of the following statements
best relates the pressures at the ends of the pipe?
A) PL = 2PR
B) PL = PR
C) PL = ½ PR
D) The relative size of PL and PR depends
on the speed of the flow.
hR
hL
PR
PL
(
1
PL - PR = rg (hR - hL ) - r vL2 - vR2
2
)
0
Mechanics Lecture 26, Slide 13