Calculator · Fluid Mechanics
Manometer Calculator
A manometer reading is a walk: start at a known pressure, then move through each fluid in turn, adding ρgΔh whenever you go down and subtracting it whenever you go up. Build the path your instrument actually follows, in order, from the first tap to the second.
Starting pressure
Gauge pressure is measured relative to the ambient pressure, so 0 kPa means ambient. It may legitimately be negative. No atmospheric pressure is added anywhere in this calculation.
Path steps, in order
Step 1
Step 2
Results
Pressure difference along the path
End pressure -123.034 kPa gauge, from a start of 0 Pa.
| Step | Fluid ρ | Move | Δp = ±ρgΔh | Pressure after step |
|---|---|---|---|---|
| 1 | 1000 kg/m³ | down 1 m | 9.80665 kPa | 9.80665 kPa |
| 2 | 13546 kg/m³ | up 1 m | -132.841 kPa | -123.034 kPa |
Assumptions
- · Each column is a static fluid of constant density.
- · Every pressure in the walk shares the reference kind of the starting pressure.
Path schematic
Schematic of the path only — the order and direction of the moves, not a scale drawing of a specific manometer. Every pressure is in the table above.
Explore in the Lab
The same ordered path, next to the pressure field it belongs to.
Technical reference
p_end = p_start + Σ ±ρᵢ g Δhᵢ
going down: Δp = +ρ g Δh
going up: Δp = −ρ g Δh
- p_start
- known pressure at the first tap[Pa]
- ρᵢ
- density of the fluid in step i[kg/m³]
- Δhᵢ
- vertical distance travelled in step i[m]
- p_end
- pressure at the far end of the path[Pa]
Only the vertical distance matters. A horizontal run inside one fluid changes nothing, which is why the path is entered as vertical moves rather than as tube lengths.
The step order is the order you physically travel. Reversing the path reverses the sign of the total.
Each step carries the density of the fluid actually in that leg. A mercury leg in a water system is a separate step with the mercury density.
The result is stated in whatever reference the starting pressure was: a walk changes pressure, never the reference it is measured against.
This is a general pressure walk, not a model of one particular instrument. A U-tube, an inclined tube and a differential manometer are all just different sequences of these steps.