# Fluids 7.1 - pressure density pascal depth buoyancy

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```					Pressures in Fluid Systems
Problem Types / Formulas
•   Density ρ = m/v
•   Pressure    P = F/A
•   Pressure at depth    P = ρhg
•   Buoyancy Force Fb= ρVg
•   Pascal’s     F1/A1 = F2/A2
States of Matter
The Fluid State:
• gases or liquids
• no definite shape
• flow
The Solid State:
• definite shape
• support a force
Density
• Density: the mass per unit volume of a
substance
ρ = m/V

• Units: kg/m3 or g/cm3
Pressure: A force distributed over an
area
P = F/A

Pressure = force / area

Units = Pascal (N/m2)
kPa or MPa
Example
• A 500 kg box is resting on the ground.
The side touching the ground is 1 m wide
by 2 m long. What’s the pressure
exerted by the box on the ground?
P = F/A
= ( 500 kg x 9.8 m/s2) / (2m x 1 m)
= 4900 N / 2 m2
= 2450 Pa
Example
A car weighs 8800 N. Each tire has a contact
patch (footprint) of 15 by 25 cm. What
pressure is exerted by the car on the ground?
P = F/A
Area = (0.15 m)∙(0.25 m)∙4 tires
A= 0.15 m2
P = 8800 N / 0.15 m2
= 58,667 Pa
= 5.9 x 104 Pa
P = 59 kPa
Gas or Air Pressure
• Kinetic Molecular Theory: as gas
particles hit a surface, they apply a
force over a tiny area.
• Lots of particles = detectable pressure.
• Gage pressure: reads zero at
atmospheric
• Absolute pressure = 101.3 kPa + Gage
Pressure
Pascal’s Principle
• Applying pressure at any point to a fluid
is transmitted immediately to the rest
of the fluid.
• Examples:
Toothpaste
Squeeze a balloon
Hydraulic jack
Hydraulic Jack

Pressure is the same throughout the fluid
F1 / A1 = F2 / A2
Pressure Underwater
• Due to weight of column of water
• Use density to simplify to:
P = ρgh
• Pressure = density x gravity x height or
depth
• ρ = “rho” = density = mass per unit
volume
Buoyancy
• Given an object underwater
• Pressure is less at the top of the object
than at the bottom.
• Result: net upward force on the object
= Buoyant Force
Buoyancy

P = ρgh1
Fnet = Fb

P = ρgh2
Buoyant Force
• Buoyant Force Fb = ρVg
Fb = (density x volume x gravity)
Fb = weight of displaced fluid
(Archimede’s)
• Compare weight of object to Fb to see if
it sinks.
Example
A block of aluminum has a volume of 0.5
m3. If it is suspended by a string in
water, which has a density of 1000
kg/m3, and g=9.8 m/s2, what is the
buoyant force acting on the block?
Fb = ρVg
= 1000 kg/m3 x 0.5 m3 x 9.8 m/s2
= 4900 N

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