Density and pressure (4.3)

What is density?

Density - mass per unit volume of an object

ρ = m/v

Where ρ is density in Kgm^-3

Where m is mass in Kg

Where v is volume is m³

What is pressure?

Pressure - force per unit area

p = F/A

Where P is pressure in Nm^-2 / Pa

Where F is force in N

Where A is area in m²

Thus if force is spread over a larger area there will be a lower pressure

What is hydrostatic pressure?

Hydrostatic pressure - the pressure at any given point within a fluid, that is exerted by the weight of the fluid above that point

If a fluid is at rest then all points within it are in equilibrium and the pressure acts in all directions at each point

What is the equation for hydrostatic pressure and how is it derived?

Derivation

The weight of the fluid above the object with area A, can be given as:

W = mg

Using the density equation, mass can be found:

ρ = m/v

m = ρv = ρAh - where h is the depth of the object under the surface of the fluid

Thus:

W = ρAhg

Thus the pressure can be given as:

p = F/A

p = ρAhg/A = ρhg

Within the cube there is a difference in pressure between the top and bottom surfaces:

∆p = ρ∆hg

Equation

∆p = ρ∆hg

Where ∆p is the change in pressure in Pa

Where ρ is the density of the fluid in Kgm^-3

Where ∆h is the change in height in m

Where g is the gravitational field strength in NKg^-1

What is a u-tube manometer?

U-tube manometer - instrument to measure density and pressure of two liquids

1 - the level is equal because the atmospheric is the same

2 - the pressure rose on one side (someone blowing into the tube), forcing the liquid on that side down and on the other up

3 - now it has two different liquids, with B being more dense but the pressure is still the same

What is upthrust?

Upthrust - the resultant force on an object submerged in a fluid due to the pressure difference between the top and bottom surfa

What is Archimedes’ principle?

Archimedes’ principle - when an object is totally or partially immersed in fluid at rest, it has an upthrust equal to the weight of the fluid displaced by the object

So when object float the upthrust equals the weight of the object

How can upthrust be calculated?

U = ρvg

Where U is upthrust in N

Where ρ is density in Kgm^-3

Where v is volume in m³

Where g is gravitational field strength in NKg^-1