A piezometer is connected to a point in a pipe to measure the pressure of water flowing through it. If the piezometer reads 0.4 m, what will be the gauge pressure at that point?

Take atmospheric pressure = 101325 pascals and g = 10 m/s² 

Concept:

Pascal's Law (Hydrostatic Law):

• In a fluid at rest, the pressure at any point is the same in all directions, and it acts equally in all directions.
• The pressure in a fluid increases with increasing depth. This is because the weight of the fluid above a given point exerts a force, leading to an increase in pressure at deeper levels.
• At any given depth, the pressure is the same in all directions. This means that at a specific depth within the fluid, the pressure acts equally on all sides of that surface.
• The hydrostatic pressure is independent of the shape of the container.

The mathematical expression of the hydrostatic pressure distribution is given by:

P = P0 + ρgh

where: P is the pressure at a depth h below the surface, P0 is the atmospheric pressure at the surface of the fluid, ρgh = gauge pressure, ρ is the density of the fluid, g is the acceleration due to gravity, h = depth or height of the fluid column.

Calculation:

Given:

Density of water, ρ = 1000 kg/m³, h = 0.4 m, g = 10 m/s2

Gauge pressure = ρgh = 1000 × 10 × 0.4 = 4000 pascals