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Density, ρ = m/V pressure, p = F/A, and Pascal’s principle buoyancy equa?on of con?nuity Bernoulli’s equa?on • applica?ons today PHYSICS 101 help sessions & oﬃce hours for Dr. Heiner Monday Tuesday Wednesday 10 – 11 AM Thursday Friday oﬃce hours HENN 405 11AM – 12PM TA help sesssion HEBB 13 12 – 1 PM TA help sesssion HEBB 13 1 – 2 PM 2 – 3 PM PHYS 101 sec?on 102 3 – 4 PM oﬃce hours HENN 405 4 – 5 PM TA help sesssion HEBB 13 PHYS 101 sec?on 102 TA help sesssion HEBB 13 TA help sesssion HEBB 13 PHYS 101 sec?on 102 TA help sesssion HEBB 13 Two Questions
Assume that water flows through a round pipe with a
certain flow rate Δm/Δt (or ρ ΔV/Δt).
At some point the diameter of the pipe decreases to half
of its former value.
Q1) The acceleration of the fluid in the narrow section
A. increases.
A1
A2
B. decreases.
C. remains the same.
Q2) The force of the fluid in the narrow section
A. increases.
B. decreases.
C. remains the same. 3 Question
The unknown (?) volume flow rate
through the pipe is: A. 0.5 cm3/s
B. 1.0 cm3/s
C. 5.0 cm3/s
D. 1.0 cm3/s
E. 2.0 cm3/s changing flow dynamics in a pipe
different diameter A1 v1 = A2 v2 equation of
continuity For constant density Δh
different heights
2 P + 1 2 ! v + ! gh = const Bernoulli’s
equation breakdown Bernoulli’s
2 P + 1 2 ! v + ! gh = const Bernoulli’s
equation if add a stopper, how
would that affect the equation? Δh
0 2 P + 1 2 ! v + ! gh = const P + ! gh = const What about a flowing fluid in a straight pipe (i.e., no Δh) ? Worksheet
Typical blood pressure in an aorta is 13,600 Pa
and its speed is 0.12 m/s. Blood passes through
an area of aorta that has been narrowed down
by plaque to a crosssectional area 1/5 of
normal aorta.
(a) What is the blood pressure as the blood passes
the narrow part?
(b) What is the percentage change in the pressure? blocked Ques?on A blood platelet driTs along with the ﬂow of blood through an artery that is par?ally blocked by deposits. As the platelet moves from the wide region to the narrow region, it experiences A. an increase in pressure blocked B. no change in pressure C. a decrease in pressure Special Case – Venturi Effect y1 = y2 Horizontal Pipe 12
12
P + ρ v1 = P2 + ρ v 2
1
2
2
12
P + ρ v = constant
2
• In the region where the fluid speed increases the pressure
in the fluid decreases.
• In the region where the fluid speed decreases the pressure
in the fluid increases. Venturi Meter
• Measures pressure by reading the height of a fluid
column. v1 A1
• velocity pressure A2 v2
v p v1 A1
v p • Height of the column in the small vertical tubes
determined by the difference in pressure due to
flowing fluid on the bottom and atmospheric pressure
on top: measures gauge pressure.
10 Prairie
Dogs V1 Burrows V2 Question Consider a straw in a glass of water.
What happens to the water level in the straw
if you blow horizontally across the top of the straw?
1) The water level drops.
2) The water level rises.
3) The water level stays the same. Bernoulli s Principle
• The velocity of a fluid is high
in regions of low pressure,
and small in regions of high
pressure.
• Applications of Bernoulli s
principle: shape of airplane
wings, curved profile of sails,
frisbee, jumping coins,
jumping eggs, etc. 14 Ping Pong Ball
Why does the ping pong
ball try to return to the
center of the jet?
What forces are acting on
the ball when it is not
centered on the jet? Worksheet
The drinking fountain outside your
classroom shoots water about 16 cm
straight up in the air from a nozzle of
diameter 0.60 cm. The pump at the base
of the unit (1.0 m below the nozzle)
pushes water into a 1.8cmdiameter
supply pipe that goes up to the nozzle. 1. air 0.16 m
2. pipe 1.0 m Using the equation of continuity and
Bernoulli’s equation, we will fill in the
table below.
pump 0.0 m 3. ...
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 Winter '08
 BATES
 Physics, Buoyancy

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