SME
Hydrology · Problem type
Hydraulic head from elevation and pressure
Use this for “A piezometer’s screen is 120 m above sea level, and the water pressure there is 98.1 kPa. Find the pressure head and the total head.”
Diagram
ψ
=
p
γ
=
98.1
9.81
=
10
m.
h
=
z
+
ψ
=
120
+
10
=
130
m.
Water rises in the pipe to the total head; heights to scale from the datum.
This is an example. Type your own values to start a new problem.
ψ (m)
=
p (kPa)
÷
ρg
h (m)
=
z (m)
+
ψ (m)
Formulas
ψ
=
p
9.81
10
=
98.1
9.81
h
=
z
+
ψ
130 = 120 + 10
Assumptions
•
Fresh water: ρ = 1,000 kg/m³ and g = 9.81 m/s², so ρg = 9.81 kN/m³ and p in kPa ÷ 9.81 gives meters.
•
Elevations and heads are measured from one datum, often sea level.
•
Water in the piezometer rises to the total head; groundwater flows from high total head to low.
Step-by-step
WE KNOW
z = 120 m, p = 98.1 kPa
FIND
pressure head (ψ), total head (h)
Step 1 · Find pressure head (ψ)
Use ψ = p ÷ 9.81
Divide
the
pressure
by
water’s
weight
per
cubic
meter,
ρg
=
9.81
kN/
m
3
.
ψ
=
98.1
9.81
ψ
=
10
m
Step 2 · Find total head (h)
Use h = z + ψ
Add the elevation and the pressure head.
h
=
120
+
10
h
=
130
m
Check
Put the numbers back in. Both sides should match.
10
=
98.1
9.81
✓
130 = 120 + 10 ✓
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