PRESSURE/FLIGHT UNIT SOME NOTES… ALL stuff we know already!!
Density is Mass /Vol (in Kg/3) for Physics
So Mass = Dens * Volume, Since Weight = Mass *g, Weight=Dens*Vol*g
Pressure is Force/Area in Newtons/ square meter
1 N/m2 = 1 Pascal of Pressure, Sea Level = 101320 Pascals
Since Energy is Force * Distance = Work
Pressure = (Force/Area * Distance/Distance)
= (Force * Distance) / (Area*Distance)
Pressure = Work / Volume = Energy/Volume
For an object in a fluid the pressure on top of it is:
Δ Pressure = Force/Area = Weight/Area
= (Dens * Vol*g)/ Area
= Dens * g * Vol/Area
Δ Pressure = Dens*g*Height
That’s the same as saying that ΔWork/Volume = mgh /Volume !
In fact the conservation of energy for a fluid is:
ΔWork + Δ GPE + Δ KE = 0 (with no heat) but dividing by volume
(Mass/Vol = Dens)
F*dist/Vol + mgh/Vol + ½ m vel2 / Vol = F*dist/Vol + mgh/Vol + ½ m vel2/ Vol
Pressure1 + Dens*g*h1 + ½ Dens*Vel12 = Pressure2 + Dens*g*h2 + ½ Dens*Vel22
This is called Bernoulli’s Principle, and is just a restatement of conservation of energy that relates Pressure (instead of work), Height and Velocity for a fluid.
If velocity stays the same, then pressure changes depending on density and height.
If height stays the same, then the faster the velocity, the lower the pressure!
Pg 337 #1
A large storage tank open to the atmosphere at the top and filled with water, develops a small hole at a point 16 m below the water. If the rate of flow of water from the leak is .0025 m3 / min, determine the following:
a) the speed at which the water leaves the hole.
b) the diameter of the hole (hint : Area = Volume/Dist= πr2 )
#3 When a person inhales, air (Density is 1.29 kg/m3 ) moves down the windpipe at 15 cm/s (.15 m/s) . The average flow speed doubles when passing through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction
1) The time required to fill a bucket with water from a certain garden hose is 30 sec. If you cover part of the hose’s nozzle with your thumb so that the speed of water leaving the nozzle doubles, how long does it take to fill the bucket?
3) The water supply of a building is fed through a main entrance pipe that is 6 cm in DIAMETER. A 2 cm DIAMETER faucet tap positioned 2 m above the main pipe fills a 25 L (25 kg) container in 30 seconds. Water is 1000 kg/m3
a) What is the speed at which water leaves the faucet?
b) What is the gauge pressure in the pipe? (Pressure compared to atmosphere)