Measuring Fluid Pressure

Sample data: Alcohol

Height (m) Pressure (Pa)

0.13 1000

0.26 2000

0.39 3000

0.52 4000

0.65 5000

0.78 6000

Slope of Pressure vs height

Slope = rise/run = Pressure/height

Pa = N = kg m = kg m

m m2m m3 sec2 m3 sec2

kg/m3 = density = ρ

m/sec2 = acceleration

Best fit equation = slope

Alcohol = 7692.3 x

Y= mx + b

Pressure = 7692.3 h + b

( b can be disregarded.

When pressure = 0 then height would = 0)

Pressure vs heightPre

ssu

re (

Pa)

Height (m)

Glycerin

Salt water

Fresh water

Alcohol

Pressure vs density using the best fit lines

Liquid Density (ρ)Kg/m3

Best fit equation

Equation at 0.4 m

Alcohol 785.4 7705 h 2830

Freshwater 1000 9810 h 3924

Saltwater 1027 10075 h 4033

Glycerin 1261 13538 h 5415

Pressure is proportional to height

P α h

and

P α ρ

So therefore:

P α ρ h × some constant C

P = C ρ h

P = C ρ h

C = P = Pa = N/m2 * m3

ρ h kg/m3 * m kg * m

= kg * m * m3

m2 * kg * m * sec2

C = m/ sec2

Finding C (using data for seawater)

P = C ρ h

C = P = 1 P

ρ h ρ h

C = 1 * 10 075

1027

C = 9.81 m/sec2

Slope

Trend line formula