Unit 1: Fluids: Pressures and Forces

Fluids

Substances which can flow.

Density

Mass per unit volume of a substance

S.I. Units of Density

kg/m³

CGS unit of density

g/cc

Pressure

Magnitude of normal force acting per unit area

S.I. Units of Pressure

Pascal

Hydrostatic pressure

Pressure due to liquid

Factors that hydrostatic pressure depends on

Density of liquid and depth below the surface

What principle does buoyancy use?

Archimedes Principle

Buoyancy

If a body is fully or partially immersed in a fluid, it experiences an upward force due to the fluid called buoyant force.

An object with a mass of 150 kg and a volume of 0.75 m3 is floating in ethyl alcohol, whose density is 800 kg/m3. What fraction of the object’s volume is above the surface of the fluid?

Volume Flow Rate

Volume of fluid that passes through a particular point per unit of time.

Formula for volume flow rate

F = Av

A = cross-sectional area

v=flow speed

Continuity equation

The density of fluid is constant. Thus, A1V1 = A2V2.

A circular pipe of non-uniform diameter carries water. At one point in the pipe, the radius is 2 cm and the flow speed is 6m/s. What is the flow speed at a point where the pipe constricts to a radius of 1 cm?

Bernoulli’s effect

At comparable heights, the pressure is lower where the flow speed is greater.

Bernoulli’s Equation

Buoyancy diagram for object floating in liquid.

Practical units for pressure

atm, bar, torr

A vertical column made of cement has a base area of 0.5 m2. If its height is 2 m, and the density of cement is 3000 kg/m3, how much pressure does this column exert on the ground?

SI unit for Volume Flow Rate

m³/s

A circular pipe of non-uniform diameter carries water. At one point in the pipe, the radius is 2 cm and the flow speed is 6m/s. What is the volume flow rate?

What does Bernoulli’s Equation assume for the conservation of energy in fluids?

The fluid is incompressible.

The fluid’s viscosity is negligible.

The fluid is streamlined.

Bernoulli’s Equation

Explain how airflow affects the airplane wing in the image and helps it fly.

The air on the bottom has greater pressure and pushes up on the wing, giving the airplane lift force.