Transcript Apr 10 Discussions

Apr 16 Discussions
Hydraulic equilibrium
Pressure and depth
Q1: Pressure
• Which of the following situations represents the
greatest pressure?
(Recall that P=F/A)
A) the weight of 10 tons on 1.0 square meter
B) the weight of 100 kg on 100 square centimeters
C) the weight of 1.0 kg on 1.0 square centimeter
D) the force of your pencil (say, 1 Newton) on its
point
Q1: Pressure
• Which of the following situations represents the
greatest pressure?
(Recall that P=F/A)
D) the force of your pencil (say, 1 Newton) on its
point:
P = F/A = (1 N)/(1 mm)2=106 Pa?
P1: Hydraulic lift
• Because of your physics knowledge, you are
asked to advise on the design of a hydraulic lift
in a car repair garage that must be able to hold a
3 ton vehicle. The piston that supports the
vehicle platform has a diameter of 30 cm and a
mass of 1 ton. A pump pushes fluid into the
piston’s cylinder through a 3 cm diameter pipe.
• What is the minimum pressure that needs to be F
exerted on the bottom of the piston to support
the vehicle?
• What is the minimum force that the piston on the
pump needs to exert on the fluid entering the
pipe to hold the vehicle in place?
Use g=10 m/s2
W
Hydraulic lift-2
• The force the large piston supports is its own weight plus the
weight of the vehicle (4 ton=4000 kg):
Wtot=mtot g = (4000 kg)(10 m/s2)=40 kN
P = Wtot/A = (40 kN)/( (0.15 m)2)=5.7x105 Pa
• The small piston needs to be able to sustain this pressure. The
force necessary is:
F = P•Apipe= (5.7x105 Pa)( (0.015 m)2)=400 N
• Another way to see this is that since the pipe has 1/100 of the
cross-sectional area of the large piston, the necessary force is
1/100 of the total weight
(40 kN)/100 = 0.4 kN = 400 N.
Note that this is about 90 lb.
P2: Pressure below the surface
• You are designing a deep sea exploration vessel. From P201
you recall that pressure increases as you go beneath the
surface of the ocean, the pressure of the atmosphere at sea
level is approximately 100 kPa, and the density of water is 1025
kg/m3.
• What pressure does your vessel need to withstand if it is to
reach at the deepest part of the ocean (about 10 km deep)?
• Metals such as titanium have compressive strengths over 500
MPa, but metals are not transparent and you want your vessel
to have a window. Glass has a compressive strength of
approximately 50 MPa. What do you recommend about
providing the ability to pressurize your vessel?
Pressure below the surface-2
• The pressure is
rgd+Po
=(1025 kg/m3)(10 m/s2)(10000m)=108 N/m2=100 MPa
(about 1000 atm), since every 10 meter of depth is equivalent to
an extra atmosphere-equivalent of pressure.
• Your window will not be able to withstand this unless you
pressurize your vessel to over 50 MPa (so the pressure
difference is less than 50 MPa). It would be best to do this
gradually on the way down (you don’t want it to be 50 MPa
internally at the surface, since your window would blow out!)
P3: Water Supply 1
• Water supplies are pressurized for several reasons,
but to provide sufficient flow, they need to be
pressurized. A city is to have a 24-inch (60 cm)
diameter supply line that is to provide
20 million gallon/day of flow (3.75 liter = 1gallon).
• What flow velocity is needed?
• According to Bernoulli’s Law, what is the minimum
pressure drop between the storage tank and the
entrance to the pipe needed to produce this velocity?
Water supply-1
• The volume flow rate=
20x106 gal/day•(3.75 liter/gal)•(1 m3/1000 liter)
=75x103 m3/day•(1 day/86400 s)=0.87 m3/s
=A•vflow=(0.30 m)2•vflow
vflow=3.1 m/s
• The pressure must obey: Ptank=Ppipe+(1/2)rv2
• The pressure drop is:
Ptank-Ppipe=(1/2)rv2=(1/2)(1000 kg/m3)(3.1 m/s)2
=5000 Pa
Water supply-2
• The end of the city water supply pipe is 60 meter above
the entrance to the pipe. A pump provides the necessary
pressure. What pressure is required at the exit of the
pump for the water to reach city, if the pressure at the
city end needs to be at least 200 kPa?
Water supply-2
• The end of the city water supply pipe is 60 meter above
the entrance to the pipe. A pump provides the necessary
pressure. What pressure is required at the exit of the
pump for the water to reach city, if the pressure at the
city end needs to be at least 200 kPa?
• Ppump+rghpump=Pcity+rghcity
Ppump=Pcity+rg(hcity-hpump)
=(200 kPa)+(1000 kg/m3)(10 m/s2)(60 m)=800 kPa