Download Physics 101 – Fluids Fluids and Density A fluid is simply a

Physics 101 – Fluids
Fluids and Density
A fluid is simply a substance that flows. It can be either a liquid or a gas. They take
the shape of the container they are in.
The density of a substance () is defined as its mass per unit volume
=m/V
The SI unit for density is kg/m3 but it is sometimes given in g/cm3
For example, with unit conversions the density of aluminum is either 2.70 g/cm3 or
2700 kg/m3.
What is the mass of an iron wrecking ball with a radius of 18 cm. ( = 7800 kg/m3)
The specific gravity of a substance is defined as the ratio of the density of that
substance to the density of water at 4.0° C. ( = 1.00 g/cm3 = 1000 kg/m3) That
means the specific gravity of iron is 7.8.
Pressure in fluids
Pressure is defined as force (perpendicular) per unit area. A fluid can exert pressure
in any direction. It exists at all points in the fluid, not just the walls of the container.
Pascal's principle : Pressure applied to an enclosed fluid is transmitted
undiminished to every part of the fluid, as well as to the walls of the container.
Pressure = P = F / A
The SI unit of pressure is N/m2, also called a pascal (Pa). (1 Pa = 1 N/m2)
Calculate the pressure of your feet on the floor when you’re standing. An average
person has a foot area of around 250 cm2. What is the pressure if you stand on one
foot? What happens for a female who wears spike heels?
In a liquid, pressure increases with depth below the surface. In a gas, the pressure is
nearly the same at all points.
Pressure in Liquids
In a liquid, the liquid above a point pushes down while the liquid below pushes up.
As you go deeper in the liquid, the liquid above becomes more and the liquid below
becomes less.
 = o + gd = pressure of air above the fluid + pressure caused by the fluid itself
(where o = 1 atm (101.3 kPa), g = gravity, and d=depth below the surface)
A submarine cruises at 300 m below the surface of the ocean. What is the pressure
on the submarine at this depth? (density of seawater = 1030 kg/m3)
Buoyancy
An object floats because of a buoyant force, the upward force of a liquid.
Fnet = Fup – Fdown = FB - Fg
If the buoyant force is greater than gravity, the thing will float.
Archimedes principle.
A fluid exerts an upward buoyant force, FB, on an object immersed in or floating on
the fluid. The magnitude of the buoyant force equals the weight of the fluid
displaced by the object.
FB = f Vf g
A dive team what to recover a submerged statue from the bottom of the sea. The
statue has a mass of 70.0 kg and a volume of 3.0 x 104 cm3. How much force is
necessary to bring the statue to the surface? ( = 1.025 x 103 kg/m3 for sea water)
Fluid Flow and the Continuity Equation
Fluids, by definition can flow, but are essentially incompressible. This provides
some very useful information about how fluids behave when they flow through a
pipe or a hose. Consider a hose whose diameter decreases along its length. The
``continuity equation'' is a direct consequence of the rather trivial fact that what
goes into the hose must come out. The volume of water flowing through the hose
per unit time (i.e. the flow rate at the beginning must be equal to the flow rate at the
end or in fact anywhere along the hose. Moreover, the flow rate at and point in the
hose is equal to the area of the hose at that point times the speed with which the
fluid is moving:
Flow rate = (area) x (velocity)
For unit analysis: m3/s = m2 x m/s
These considerations lead us directly to the continuity equation, which states that
(area) x (velocity) = constant
everywhere along the hose. This has the important consequence that as the area of
the hose decreases, the velocity of the fluid must increase, in order to keep the flow
rate constant. Anyone who has pinched one end of a garden hose has experienced
this effect: the smaller you pinch the end of the hose, the faster the water comes out.
A 25 mm diameter hose needs to fill a 20 L bucket in 40 s. What is the flow rate of
the water in the hose? If a nozzle with a diameter of 5 mm is put on the end of the
hose what is the velocity of the water as it is sprayed.
Fluid Dynamics
When fluid are given the chance to move with different velocities with an area,
strange things can happen, a pressure gradient is created.
Bernoulli Effect – the pressure is higher at a point along a streamline where the
fluid is moving slower and lower where the fluid is moving faster.
In an aircraft wing, the air moving above and below the wing travel at different
velocities when the aircraft is in flight. The faster air moving above the wing creates
a lower pressure than the slower air below the wing. This helps create lift and keeps
the aircraft flying. Turn the wing upside down and put it on the back of a race car
and you get an airfoil that helps keep the car on the road at high speeds. It also
makes sailboats sail into the wind and curves a baseball.
Bernoulli’s Equation
This relates to the Law of Conservation of Energy and fluids. When fluids change
height and/or speed, the total energy in the fluid needs to remain constant.
P + ½  v2 +  g y = constant (where y = change in height of the fluid)
You often see the equation written:
P1+ ½  v2 +  g y1 = P2+ ½  v2 +  g y2
A house has a hot water heating system. Hot water is pumped at 0.50 m/s through a
4.0 cm pipe in the basement under a pressure of 3.0 atm. What is the flow speed and
pressure in a 2.6 cm pipe on the second floor 5.0 m above the basement. Assume the
pipes do not divide.