Transcript 3) Hydraulic Lift

Fluids examples
1.
Hydrostatic pressure calculation
height of water level above bottom = 158.5 meters
What is the pressure at the bottom?
2. Ship displacement 810 million N!
How many cubic meters of water are displaced by the
ship?
(How much volume of the ship’s hull is below the
waterline?)
3) Hydraulic Lift
a) What mass truck can F lift?
F = 500 N
40 cm
F2
A
5 cm
F1
a
A/a = 100
b) If piston a moves 1 cm /sec, how fast does the truck rise?
Use your knowledge of equilibrium, (beams) to get F2
Sum of torques = 0 = 40 F1 +5 F2
Use Pascal’s Principle to get Max Lift Force.
P
F1 F2

A1 A 2
Use Continuity to get lift speed.
A1v1 = A2v2
4) Hoover Dam
a) What is the velocity of the
stream at the emergency outlets?
b) How far does out into the river
does the outlet stream land in the
Colorado River?
c) How fast does the level of Lake
Mead drop when all gates are
open?
8 - 173 cm dia, 4 - 229 cm dia
outlets
55 meters
Colorado River
http://www.usbr.gov/lc/hooverdam/faqs/tunlfaqs.html
Area = 640 sq km
Lake Mead
158.5 m
g = 9.8 m/sec2
a) What is the velocity of the
stream at the emergency outlets?
Down River
Start with Bernoulli’s eq’n
Lake Mead
P + 1/2 rv2 + rgh = P + 1/2 rv2 + rgh
b) How far does the stream travel
before reaching the downstream
water level?
Think back to freefall
Velocity v
55 m
d=?
dist = v t Time to fall= ???
c) How fast does the level of Lake
Mead drop when all gates are
Area of Lake Mead = 640 sq km
open?
Area of outlets = 8 x p(0.865)2 + 4 x p(1.15)2 sq m
Use v from previous exercise
Continuity
a1v1=a2v2