Unit 6 : Part 1Fluids

Overview

Pressure and Pascal’s Principle

Buoyancy and Archimedes’ Principle

Fluid Dynamics and Bernoulli’s Equation

Fluids: Pressure and Pascal’s Principle

Pressure is defined as the force per unit area:

If the force is at an angle to the surface, the more general form (blue box) is used.

Fluids: Pressure and Pascal’s Principle

Unit of pressure: the Pascal (Pa)

Density is defined as mass per unit volume:

Fluids: Pressure and Pascal’s Principle

Fluids: Pressure and Pascal’s Principle

The pressure in a fluid increases with depth, due to the weight of fluid above it.

Fluids: Pressure and Pascal’s Principle

Pascal’s principle:

Pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of the container.

Fluids: Pressure and Pascal’s Principle

Hydraulic lifts and shock absorbers take advantage of Pascal’s principle.

Fluids: Pressure and Pascal’s Principle

Since the pressure is constant, a small force acting over a small area can become a large force acting over a large area.

Fluids: Pressure and Pascal’s Principle

There are a number of methods used to measure pressure.

Fluids: Pressure and Pascal’s Principle

Absolute pressure is the total force per unit area. We often measure the gauge pressure, which is the excess over atmospheric pressure.

Atmospheric pressure historically was measured using a mercury barometer.

Fluids: Pressure and Pascal’s Principle

The pressure corresponding to 1 mm of mercury is called the torr (in honor of Torricelli).

Buoyancy and Archimedes’ Principle

A body immersed wholly or partially in a fluid experiences a buoyant force equal in magnitude to the weight of the volume of fluid that is displaced:

An object’s density will tell you whether it will sink or float in a particular fluid.

Buoyancy and Archimedes’ Principle

The buoyant force on an object that is completely submerged:

Buoyancy and Archimedes’ Principle

It is the average density that matters; a boat made of steel can float because its interior is mostly air.

An object’s density may be changed; submarines fill tanks with water to submerge, and with air to rise.

Buoyancy and Archimedes’ Principle

Specific gravity is the ratio of an object’s density to that of water at 4°C.

Fluid Dynamics and Bernoulli’s Equation

In an ideal fluid, flow is steady, irrotational, nonviscous, and incompressible.

Steady flow means that all the particles of a fluid have the same velocity as they pass a given point.

Steady flow can be described by streamlines.

Fluid Dynamics and Bernoulli’s Equation

Irrotational flow means that a fluid element (a small volume of the fluid) has no net angular velocity. This condition eliminates the possibility of whirlpools and eddy currents. (The flow is nonturbulent.)

In the previous figure, the paddle wheel does not turn, showing that the flow at that point is irrotational.

Fluid Dynamics and Bernoulli’s Equation

Nonviscous flow means that viscosity is negligible. Viscosity produces drag, and retards fluid flow.

Incompressible flow means that the fluid’s density is constant. This is generally true for liquids, but not for gases.

Fluid Dynamics and Bernoulli’s Equation

Equation of continuity:

Fluid Dynamics and Bernoulli’s Equation

If the density is constant,

Fluid Dynamics and Bernoulli’s Equation

Bernoulli’s equation is a consequence of the conservation of energy.

Fluid Dynamics and Bernoulli’s Equation

One consequence of Bernoulli’s equation, that the pressure is lower where the speed is higher, can be counterintuitive.

Fluid Dynamics and Bernoulli’s Equation

The flow rate from a tank with a hole is given by Bernoulli’s equation; the pressure at open areas is atmospheric pressure.

Review

Pressure is defined as force per unit area.

Pressure varies with depth in a fluid:

Review

Pressure in an enclosed fluid is transmitted unchanged to every part of the fluid.

The buoyant force is equal to the weight of displaced fluid.

An object will float if its average density is less than that of the fluid; if it is greater, the object will sink.

Review

Equation of continuity:

Flow rate equation:

Bernoulli’s law: