SME
Fluid Mechanics
Fluid statics
Use this for “What are the gauge and absolute pressures 15 m under water?”
Diagram
Pgauge = ρgh = 1,000 × 9.81 × 15 = 147,200 Pa.
Pabs = Pₐₜₘ + Pgauge = 101.3 + 147.2 = 248.5 kPa.
This is an example. Type your own values to start a new problem.
Pgauge (kPa)
=
ρ (kg/m³)
×
9.81
×
h (m)
Pabs (kPa)
=
Pₐₜₘ (kPa)
+
Pgauge (kPa)
Formulas
Pgauge
=
ρ
×
9.81
×
h
147,150 = 1,000 × 9.81 × 15
Pabs = Pₐₜₘ + Pgauge
248,475 = 101,325 + 147,150
Formulas are worked in Pa. The step-by-step shows the conversions.
Assumptions
•
The fluid is at rest and has the same density at every depth (incompressible).
•
g = 9.81 m/s².
•
Gauge pressure is measured from the atmosphere’s; absolute pressure adds Pₐₜₘ, 101.325 kPa at sea level.
Step-by-step
WE KNOW
h = 15 m, ρ = 1,000 kg/m³, Pₐₜₘ = 101.325 kPa
FIND
gauge pressure (Pgauge), absolute pressure (Pabs)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to Pa).
Pₐₜₘ = 101.325 kPa = 101,325 Pa (1 kPa = 1000 Pa)
Step 2 · Find gauge pressure (Pgauge)
Use Pgauge = ρ × 9.81 × h
Each metre of depth adds ρg pascals: multiply the density by g and the depth.
Pgauge = 1,000 × 9.81 × 15
Pgauge = 9,810 × 15
Pgauge = 147,150 Pa
Step 3 · Find absolute pressure (Pabs)
Use Pabs = Pₐₜₘ + Pgauge
The air presses on the surface too: add the atmosphere’s pressure to the gauge pressure.
Pabs = 101,325 + 147,150
Pabs = 248,475 Pa
Step 4 · Convert the answers
Change each answer back to the unit you chose.
Pgauge = 147,150 Pa = 147.2 kPa (1 kPa = 1000 Pa)
Pabs = 248,475 Pa = 248.5 kPa (1 kPa = 1000 Pa)
Check
Put the numbers back in. Both sides should match.
147,150 = 1,000 × 9.81 × 15 ✓
248,475 = 101,325 + 147,150 ✓
Topic check
See what you know: 5 questions on this topic
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