Forces in Fluids

Pressure• Pressure is equal to the force

applied to a surface, divided by the area.

Equations for Pressure

•Pressure = Force/surface area

•Pressure = Newtons (Kg x m/s/s)side x side

•Units are in Pascals or N/m²

• A substance that can easily change shape or flow.

(example: liquids and gases)•The molecules in a fluid have a certain amount of force (mass & acceleration) and exert pressure on surfaces they touch

•All the molecules add up together to make up the force exerted by the fluid.

•Air has a mass of 1Kg/m³

•Gravity creates an air pressure of 10.13N/m³ at sea level.

1 atmosphere = 760 mmHg = 29.92 inHg = 14.7 lb/in2 = 101.3 KPa

•Air Pressure decreases as elevation increases

Very Low pressure

Higher Pressure

The whole system is a low pressure, but it dramatically decreases towards the eye of the hurricane.

Pressure always flows from high to low, which creates the high velocity winds.

-A Barometer is used to measure atmospheric pressure.

- It can measure the pressure exerted by the atmosphere by using water, air, or mercury.

-Some types of Barometers are water-based, Mercury, Barographs and Aneroid.

-A barometer is commonly used for weather prediction, as high air pressure in a region indicates fair weather while low pressure indicates that storms are more likely.

-Evangelista Torricelli, who is generally credited with inventing the barometer, went on to build the first instrument with mercury in 1643.

Barometric Pressure

• The barometer is used to forecast weather.

• Decreasing barometer means stormy weather and an increasing barometer means warmer weather.

MERCURY BAROMETER

Aneroid vs. Mercury Barometer

•Water pressure increases with depth.

Water Pressure and Depth• Water pressure acts in the opposite direction

compared to air pressure• Water pressure increases as depth increases!

•When a force is applied to a confined fluid, the increase in pressure is transmitted equally to all parts of the fluid.

Transmitting Pressure in a Fluid

• When force is applied to a confined fluid, the change in pressure is transmitted equally to all parts of the fluid.

Hydraulic Devices• In a hydraulic device,

a force applied to one piston increases the fluid pressure equally throughout the fluid.

Hydraulic Devices

• By changing the size of the pistons, the force can be multiplied.

4 N

.002m2

20m

1. What is the pressure of the left piston?

2. What is the pressure of the right Piston?

2000Pa

P= F/a = 4/.002 = 2000Pa

3. What is the total force of the right Piston?

40,000NF=Pa= 2000N/m2 x 20m2 =

Hydraulic Brakes

• The hydraulic brake system of a car multiplies the force exerted on the brake pedal.

The tendency or ability of an object to float.

Buoyancy• The pressure on the

bottom of a submerged object is greater than the pressure on the top. The result is a net force in the upward direction.

Buoyant ForceThe upward force exerted by a fluid on a submerged or floating object.

Buoyancy• The buoyant force works opposite the

weight of an object.

Archimedes’ principle:• Buoyant Force acting on an object immersed

in a liquid equals the weight of the liquid displaced and the weight of the object if it floats.

• This force does not depend on the weight of the object!

Archimedes' Principle

Hmm! The crown seems lighter under water!

The buoyant force on a submerged object is equal to the weight of the liquid displaced by the object. For water, with a density of one gram per cubic centimeter, this provides a convenient way to determine the volume of an irregularly shaped object and then to determine its density

•Density and buoyancy: An object that has a greater density than the fluid it is in, will sink. If its density is less than the fluid it will float.

• A solid block of steel sinks in water. • A steel ship with the same mass floats on

the surface.

Density• Changes in density cause a submarine to

dive, rise, or float.

Density• Changes in density cause a submarine to

dive, rise, or float.

Density• Changes in density cause a submarine to

dive, rise, or float.

1g/cm³

•The pressure exerted by a moving stream of fluid is less than its surrounding fluid.

•Therefore, as the speed of the fluid increases its pressure decreases.

A non-spinning baseball or a stationary baseball in an airstream exhibits symmetric flow. A baseball which is thrown with spin will curve because one side of the ball will experience a reduced pressure. This is commonly interpreted as an application of the Bernoulli principle. The roughness of the ball's surface and the laces on the ball are important! With a perfectly smooth ball you would not get enough interaction with the air.

Bernoulli’s and Baseball

The air across the top of a conventional airfoil experiences constricted flow lines and increased air speed relative to the wing. This causes a decrease in pressure on the top according to the Bernoulli equation and provides a lift force. Aerodynamicists (see Eastlake) use the Bernoulli model to correlate with pressure measurements made in wind tunnels, and assert that when pressure measurements are made at multiple locations around the airfoil and summed, they do agree reasonably with the observed lift.

Bernoulli’s and Air Foil

• Others appeal to a model based on Newton's laws and assert that the main lift comes as a result of the angle of attack. Part of the Newton's law model of part of the lift force involves attachment of the boundary layer of air on the top of the wing with a resulting downwash of air behind the wing. If the wing gives the air a downward force, then by Newton's third law, the wing experiences a force in the opposite direction - a lift. While the "Bernoulli vs Newton" debate continues, Eastlake's position is that they are really equivalent, just different approaches to the same physical phenonenon. NASA has a nice aerodynamics site at which these issues are discussed.