# Hydrostatic Pressure vs. Shear Stress: What Is the Difference?

### Key Takeaways

• Hydrostatic pressure can be described as the pressure exerted by a fluid at rest due to the force of gravity.

• The hydrostatic pressure is proportional to the depth of the fluid measured from its surface.

• On a given horizontal plane, the hydrostatic pressure is the same at all points. The pressure exerted by water, otherwise called hydrostatic pressure, is a major cause of basement water problems

Have you ever experienced water in your basement? The pressure exerted by water, otherwise called hydrostatic pressure, is a major cause of basement water problems. The water exerts immense hydrostatic pressure against the foundation and can leak through even a hairline crack in the basement.

Hydrostatic pressure affects different aspects of our daily life; in fluid dynamics, hydrostatic pressure and shear stress are often mistaken, as both are unit area amounts of force. It is important to understand the difference between hydrostatic pressure vs. shear stress in fluids to develop complex engineering systems. Let’s explore hydrostatic pressure and shear stress further.

## Hydrostatic Pressure in Fluids

All states of matter exert pressure, and in fluids (liquids and gases), the exerted pressure is equal on all sides of the container. The pressure that is exerted by a fluid per unit area of the contact surface is called hydrostatic pressure. Hydrostatic pressure can be otherwise described as the pressure exerted by a fluid at rest due to the force of gravity. Hydrostatic pressure is the internal pressure exerted by a non-moving fluid on itself. At any point in time, a fluid at equilibrium exerts hydrostatic pressure. Hydrostatic pressure is a scalar quantity that remains constant regardless of the direction. The unit of measurement of a hydrostatic system is Pascal in the International system and pounds per square inch (psi) in the English system.

## Hydrostatic Pressure Depends on Depth and Density

The hydrostatic pressure is proportional to the depth of the fluid measured from its surface. As the depth increases, the weight exerted by the downwards fluid increases and boosts the hydrostatic pressure. Hydrostatic pressure (P) exerted at any point in a fluid can be calculated using the equation: is the fluid density, g is the gravitational constant, and h is the height of the column of liquid above the measurement point. The deeper we get in a fluid, the greater the hydrostatic pressure. In a container, the hydrostatic pressure increases with an increase in depth, and maximum hydrostatic pressure is experienced at the bottom of the container. With density variations, the hydrostatic pressure also changes. Denser fluids exert more hydrostatic pressure than less dense fluids.

In a continuously distributed uniform static fluid, the hydrostatic pressure varies only with vertical depth and is completely independent of the shape of the container. On a given horizontal plane, the hydrostatic pressure is the same at all points.

### The Real World Significance of Hydrostatic Pressure

Hydrostatic pressure is exerted on any type of fluid. All static fluids, such as air, water, acids, etc., experience this pressure. The hydrostatic pressure of air changes with elevation, which is why deep sea diving is so dangerous and the air on mountain tops or on airplanes is so thin. In the human body, hydrostatic pressure is crucial for circulating blood, keeping our lungs properly inflated, and preventing the vaporization of water from our bodies.

## Hydrostatic Pressure vs. Shear Stress

Hydrostatic pressure can be regarded as a state of stress with equal stresses acting in all directions. Hydrostatic pressure is often confused with shear stress, as both are defined as a unit area amount of force. However, there is a difference between hydrostatic pressure and shear stress: hydrostatic pressure is exerted on fluids at rest.

Fluids at rest have normal stress and fail to resist shear stress. In a fluid at rest, the sum of all the forces balances the weight of the fluid, and the condition is considered hydrostatic. Hydrostatic pressure is the only normal stress that acts inwards, towards, and perpendicular to the surface.

When fluid is in motion, it experiences normal stress and shear stress. The shear stress acting on the fluid is tangential stress. It acts parallel or along the surface. Friction due to fluid viscosity is a major cause of shear stress in fluid. When shear stress is applied to fluids at rest, they start to move. Shear stress is always associated with deformation and is the ideal parameter for differentiating between solids and fluids.

A thorough understanding of the difference between hydrostatic pressure vs. shear stress is critical when dealing with fluid statics and fluid dynamics. Cadence’s suite of CFD tools can help you model systems where fluids are in motion or at rest.