## October 23, 2011

### 5.6 Pressure Difference

Recall and use the relationship for pressure difference:

Δp = pressure of the fluid (N/m2 or Pa)
h = Height of the fluid above loci (depth) (m)
ρ = density of the fluid (kg/m3)
g = gravitational field strength (N/kg)

Proof

• The bottom hole of this column squirts water the furthest
• This is because the water at the bottom has more pressure
• In the formula: Δp = hρg, ρ and g are both constant at all loci, but h is larger lower down \Δp = large.

Questions

The pressure gauge on a submarine in a river was reading 100kPa when it was the surface. If a sailor notices that the gauge is now reading 250kPa, how deep is he? How would the answer change if he were diving in sea water that is slightly denser that fresh water?
Note: ρfresh water = 1,000kg/m
3

$150,000Pa=h\times 1,000kg/m^{3}\times 10N/kg$
$h=150,000/10(1,000)$
$h=15m$

If the submarine was in sea water he would be slightly shallower than 15m.

A diver on Saturn’s moon Titan is 50m below the surface of a lake of liquid methane, what is the increase in pressure on him due to his depth in the methane? The density of liquid methane is 0.42g/cm3. The acceleration of gravity on Titan is 1.4m/s2.
We are told that the pressure of the atmosphere on Titan is 1600mbar. What is the total pressure on the diver (in kPa)?
Note: 1000mbar = 1bar = 100,000Pa.

$\rho = 0.43g/cm^{3}=420kg/m^{3}$
$\Delta p=50\times 420\times 1.4$
$\Delta p=29,400Pa=29.4kPa$

$1600mbar=1.6bar=160,000Pa=160kPa$
$Total\: Pressure=19.4kPa+160kPa$
$Total\: Pressure=189.4kPa$