1.3 Fluids: Pressure and Forces

1.3 Fluids: Pressure and Forces

Pressure

What is Pressure?

Pressure is a measure of force distributed over an area. In fluid dynamics, it is calculated as the ratio of the force to the perpendicular area of an object. This property is typically measured in units such as atmospheres (atm) or Pascals (Pa).

Key Formula:

Where:

• : Pressure (Pa or atm)

• : Force (N)

• : Area (m²)

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted on an object submerged in a fluid due to the fluid’s weight.

Key Formula:

Where:

• : Hydrostatic pressure

• : Density of the fluid (kg/m³)

• : Acceleration due to gravity (m/s²)

• : Depth below the fluid’s surface (m)

Important Notes:

• Hydrostatic pressure depends only on the density of the liquid and the depth of the object, not its mass.

• Total (or absolute) pressure is the sum of gauge pressure and atmospheric pressure:

If atmospheric pressure is not explicitly given, it is typically assumed to be 1 atm.

Gauge Pressure Example:

Q: What is the gauge pressure in an open fish tank if the absolute pressure is 5 atm?
A: Gauge pressure = Absolute pressure – Atmospheric pressure = 5 atm – 1 atm = 4 atm.

Pascal’s Principle

Pascal’s principle states that the pressure applied to a confined fluid is transmitted equally and undiminished throughout the fluid and to the walls of its container.

Key Applications:

• Hydraulic lifts

• Hydraulic brakes

• Hydraulic presses

Key Points:

• Allows a small force applied over a small area to exert a larger force over a larger area.

• Based on the conservation of energy and the equation of state for fluids.

Pressure and Velocity: The Bernoulli Effect

The Bernoulli effect describes the inverse relationship between pressure and velocity in a moving fluid. High-velocity fluids exert lower pressure, while low-velocity fluids exert higher pressure.

Key Formula:

Where:

• : Pressure

• : Fluid density

• : Fluid velocity

• : Acceleration due to gravity

• : Height above a reference point

Key Observations:

• Explains the lift generated by airplane wings and the curve of a spinning golf ball.

• Demonstrates that faster-moving fluids exert less pressure on the container walls.

Practical Example:

• Airplane flight: The difference in air velocity above and below the wing creates lift. ✈️

• Golf ball flight: Dimples on the ball exploit the Bernoulli effect for controlled lift and spin.

Additional Insights

Cautions About Pressure:

• Unlike force, pressure is scalar and acts perpendicular to a surface.

• Pressure at a point in a fluid is equal in all directions, a fact that is critical for hydraulic systems and supports Pascal’s principle.

Applications in Fluid Systems:

Pressure concepts form the basis of fluid mechanics, appearing later in topics like thermodynamics and gas dynamics. For now, the focus remains on interactions within liquids, with gases to follow in future units.