Pressure in Fluids
Discover how pressure at a depth depends only on density, gravity, and depth - not the container width or shape.
Pressure at 0.50m depth: 4.91 kPa
Derivation
P = F / A
F = Weight = rho * V * g
F = rho * (A * h) * g
P = (rho * A * h * g) / A
P = rho * g * h
Area (A)
1.00 m²
F_atm
101.33 kN
Weight (W)
4.91 kN
F_total
106.23 kN
Pressure at depth h
P = rho * g * h = 4.91 kPa
Independent of L!
Current Values
rho = 1000 kg/m³
g = 9.81 m/s²
h = 0.5 m
L = 1.0 m
At any fixed depth h:
Fluid weight increases with container width (proportional to L²), but area also increases (proportional to L²). Therefore, Pressure = Force / Area = rho * g * h remains constant!
Remember
At any fixed depth, the pressure is the same regardless of the container's shape or size. This principle applies to everything from water glasses to ocean depths!