13.3
Pressure of Fluids
There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather (…
Ever wondered how a fluid flows from one point to another?
To understand this, consider a fluid of constant density at rest. If a force is applied parallel to the surface of the fluid, then to accommodate this force, the fluid is set into motion.
In contrast, if a normal force is applied on the fluid's surface, an equal and opposite force develops in the fluid as a reaction. This normal force exerted by the fluid per unit area is called pressure. The SI unit of pressure is pascal.
Pressure is always normal to any surface in contact with the fluid and so is a scalar quantity. In comparison, force has a specific direction and is a vector quantity.
The pressure at a depth h from the fluid's surface is the sum of atmospheric pressure and pressure due to the fluid's weight.
When we substitute the equivalent expressions for weight, mass, and volume, we get the pressure due to the fluid's weight as the product of density, acceleration due to gravity, and h.
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Q1: What is pressure in a fluid and how is it different from force?
Pressure is the normal force exerted by a fluid per unit area, measured in pascals. Unlike force, which is a vector with specific direction, pressure is a scalar quantity with no directional component. Pressure always acts perpendicular to any surface in contact with the fluid because fluids cannot withstand shearing forces.
Q2: Why does a sharp needle puncture skin more easily than a finger applying the same force?
A needle concentrates force over a much smaller area than a finger, creating significantly higher pressure. The same force applied to 1 mm² produces 100 times greater pressure than when applied to 1 cm². This demonstrates how pressure, not force alone, determines whether a surface is penetrated or deformed.
Q3: How does pressure change with depth in a fluid?
Pressure at depth h equals atmospheric pressure plus the pressure from the fluid's weight above that point. This weight-based pressure is calculated as the product of fluid density, gravitational acceleration, and depth. In a swimming pool with constant density, pressure increases gradually with depth due to the water column above.
Q4: Why does atmospheric pressure vary differently than water pressure with height or depth?
Water density remains approximately constant, so pressure changes predictably with depth. Air density, however, changes significantly just above Earth's surface, causing variation of atmospheric pressure to follow a different pattern. This fundamental difference affects how pressure behaves in the atmosphere versus in liquid bodies.
Q5: What happens when a perpendicular force is applied to a fluid?
A perpendicular force compresses or expands the fluid, triggering a reaction force that develops at each point inside the fluid in the outward direction. This reaction force balances the applied force on the molecules at the boundary, maintaining equilibrium. This behavior is fundamental to understanding how fluids respond to external pressure.
Q6: Why is pressure always perpendicular to surfaces in contact with fluids?
Fluids cannot withstand or exert shearing forces, so they can only resist forces applied perpendicular to their surfaces. In a static fluid enclosed in a tank, forces on the walls and on any object within the fluid are always exerted perpendicular to the inner surface. This perpendicular orientation is a defining characteristic of fluid pressure.
Q7: How do fluids respond differently to parallel versus perpendicular forces?
When force is applied parallel to a fluid's surface, molecules flow freely to accommodate the horizontal force with minimal resistance. In contrast, perpendicular forces compress or expand the fluid, creating reaction forces. This difference reflects the fundamental property that fluids lack significant resistance to shearing forces but respond strongly to normal forces.