SME
Fluid Mechanics · Problem type
Differential manometer
Use this for “A mercury manometer on a water pipe reads 0.12 m. What is PA − PB?”
Diagram
ΔP = (ρₘ − ρ)gh
ΔP = (13,600 − 1,000) × 9.81 × 0.12
ΔP = 14,830 Pa
The level under the higher pressure (A) is pushed down.
This is an example. Type your own values to start a new problem.
ΔP (kPa)
=
(
ρₘ (kg/m³)
−
ρ (kg/m³)
)
×
9.81
×
h (m)
Formulas
ΔP
=
(ρₘ
−
ρ
)
×
9.81
×
h
14,830 = (13,600 − 1,000) × 9.81 × 0.12
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.
•
Taps A and B are at the same height, and the fluid in each leg above the gauge fluid is the pipe’s.
Step-by-step
WE KNOW
h = 0.12 m, ρ = 1,000 kg/m³, ρₘ = 13,600 kg/m³
FIND
pressure difference PA − PB (ΔP)
Step 1 · Find pressure difference PA − PB (ΔP)
Use ΔP = (ρₘ − ρ) × 9.81 × h
Go
down
one
leg
and
up
the
other:
only
the
h
where
the
legs
hold
different
fluids
counts,
so
use
the
difference
of
the
densities.
ΔP = (13,600 − 1,000) × 9.81 × 0.12
ΔP = 12,600 × 9.81 × 0.12
ΔP = 123,606 × 0.12
ΔP = 14,832.72 Pa
Step 2 · Convert the answers
Change each answer back to the unit you chose.
ΔP = 14,830 Pa = 14.83 kPa (1 kPa = 1000 Pa)
Check
Put the numbers back in. Both sides should match.
14,830 = (13,600 − 1,000) × 9.81 × 0.12 ✓
Topic check
See what you know: 5 questions on this topic
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