Fluid Flow Steady - velocity at any point is constant. Steady flow is called streamline flow.

Compressible (or incompressible) - Most liquids are incompressible, gases are highly compressible.

Viscous (or nonviscous) – Does not flow readily. An incompressible, non-viscous fluid is an ideal fluid.

Ideal fluids exhibit steady, nonturbulent flow. This doesn’t exist in real life, but it is the way we study fluid flow.

The equation of continuity expresses the idea that if a fluid enters one end of a pipe at a certain rate of flow, it must exit at the same rate. The mass of fluid per second is called the mass flow rate.

The mass Δm of a fluid that passes given point in a given amount of time is: Δm = ρAvΔt. The mass flow rate is: Δm/Δt = ρAv.

The mass flow rate Δm/Δt = ρAv. The mass flow rate is the same throughout a conducting tube. This is the equation of continuity.

ρ 1 A 1 v 1 = ρ 2 A 2 v 2 ρ = fluid density (kg/m 3 ) A = cross-sectional area of tube (m 2 ) v = fluid speed (m/s) The unit of mass flow rate is kg/s.

If we are dealing with an incompressible fluid, ρ 1 = ρ 2, and the equation of continuity reduces to A 1 v 1 = A 2 v 2. Av is the volume flow rate Q.

A garden hose has an unobstructed opening with a cross-sectional area of 2.85 x m 2, from which water fills a bucket in 30.0 s. The volume of the bucket is 8.00 x m 3. Find the speed of the water that leaves the hose through (a) the unobstructed opening and (b) an obstructed opening that has only half as much area.

Bernoulli’s Principle - a moving fluid exerts less pressure than a stationary fluid. Bernoulli’s equation also includes elevation, the pressure is greater at a lower level than at higher elevation.

Bernoulli’s Equation: P 1 + 1/2 ρv ρgh 1 = P 2 + 1/2 ρv ρgh 2 h is the elevation. This applies to the steady, irrotational flow of a nonviscous, incompressible fluid.

P + 1/2 ρv 2 + ρgh has a constant value at all points.

If the fluid is not moving and the original h is 0, P 1 + 1/2 ρv ρgh 1 = P 2 + 1/2 ρv ρgh 2 becomes: P 1 = P 2 + ρgh 2, the equation for the effect of depth on pressure.

If a moving fluid is in a horizontal pipe, h remains constant and the equation simplifies to: P 1 + 1/2 ρv 1 2 = P 2 + 1/2 ρv 2 2

P + 1/2 ρv 2 remains constant throughout the pipe. P 1 + 1/2 ρv 1 2 = P 2 + 1/2 ρv 2 2

In words, the greater the velocity of a fluid, the less the pressure.This is Bernoulli’s Principle, which is a special case of Bernoulli’s equation.

A water tank has a spigot near its bottom. If the top of the tank is open to the atmosphere, determine the speed at which the water leaves the spigot when the water level is m above the spigot.

An airplane wing is an example of how fluid flow affects pressure. Ski jumpers also use this principle to provide lift.

An ideal gas is an ideal model for gases that relates absolute pressure, Kelvin temperature, volume and the number of moles of the gas. PV = nRT is called the ideal gas law.

PV = nRT P is the absolute pressure V is the volume n is the number of moles T is the temperature in Kelvins R is the universal gas constant and has a value of 8.31 J/(molK)

Using the ideal gas law, one mole of an ideal gas can be shown to have a volume of 22.4 liters at 0°C and one atmosphere of pressure (standard temperature and pressure, STP).

Boyle’s law states that, if temperature and number of moles are held constant, the pressure and volume vary inversely; P i V i = P f V f.

The curve that passes through the initial and final points is called an isotherm. An isotherm at a different temperature would not intersect.

Charles law states that if the pressure and number of molecules are held constant; the volume is directly proportional to the temperature, V i /T i = V f /T f.

The ideal gas law provides no information as to how pressure and temperature are related to properties of the molecules themselves.

If the number of moles is held constant, the value PV/T remains constant for a contained gas.