Properties of Fluids

Fluids include two states of matter Liquids Gases What is a Fluid? Fluids include two states of matter Liquids Gases

Sink or Float? We have said that density is what determines whether an object will sink or float in a fluid. This is only part of the story! Another factor affecting this is called the buoyant force.

Buoyant Force Buoyant force (measured in Newtons) is the upward force exerted by a fluid on an immersed object. Buoyant force > weight Balloon rises Buoyant force < weight Balloon sinks Buoyant force = weight Balloon floats

Buoyant Force

Archimedes’ Principle The buoyant force on an object in a fluid equals the weight of the fluid displaced by the object.

Buoyant Force Determine whether each object will float or sink. 20 N

Calculating Buoyant Force of Water How much water does the object displace? (In other words, what is the volume of the object?) One cubic foot of water has a buoyant force of about 62.43 pounds. Multiply the volume of the object (in ft3) by 62.43 to find the buoyant force. If buoyant force is greater than the weight of the object, the object will float! If buoyant force is less than weight, the object will sink.

Example A cube weighing 500 lbs. and measuring 3x6x2 ft is dropped into water. Will it float or sink? First, find the volume of the cube (l x w x h). 3 x 6 x 2 = 36 ft3 Multiply by 62.43 lbs to find the buoyant force. Buoyant force = 2,247.5 lbs Compare buoyant force to the weight of the object. If Buoyant force > weight, object will float

Viscosity Liquid’s resistance to flow Depends on the attraction between particles Stronger attraction = more viscous (does not flow easily) Can be affected by temperature

Pascal’s Principle Named for French scientist Blaise Pascal Explains how pressure is transmitted through fluids Pressure = force exerted on a specific area

Pascal’s Principle stop at 1:15 Pressure applied to a fluid is transmitted throughout the fluid Example: squeezing a tube of toothpaste Example: Cartesian diver

Applying Pascal’s Principle Hydraulics machines are based on Pascal’s Principle. Transmit pressure through a fluid to multiply force Save us some work Examples: hydraulic lifts, dentist chairs, hospital beds, etc.

Hydraulics You input a small amount of force over a small area The output is a large force over a large area

Hydraulics

Pascal’s Principle We can use Pascal’s Principle to calculate how much force will result from a hydraulic device Pressure = Force/Area Measured in pascals (Pa)

Pascal’s Principle Platform: F = 1000 N A = 250 m2 Plunger: F = ? A car weighing 1000 N sits on a 250 m2 platform. What force is needed on the 10 m2 plunger to keep the car from sinking? GIVEN: Platform: F = 1000 N A = 250 m2 Plunger: F = ? A = 10 m2 WORK: 1000 N = F2 250 m2 10 m2 (1000 N)(10 m2)=(250 m2)F2 F2 = 40 N

Pascal’s Principle Platform: F = 1000 N A = 5 m2 Plunger: F = ? A disgruntled cow that weighs 1000 N sits on a 5 m² piston. What force would need to be applied to a 2 m² piston? GIVEN: Platform: F = 1000 N A = 5 m2 Plunger: F = ? A = 2 m2 WORK: 1000 N = F2 5 m2 2 m2 (1000 N)(2 m2)=(5 m2)F2 F2 = 400 N

Pascal’s Principle You apply 20 N of force to a 3 m2 piston on a hydraulic car lift. What would the area of the platform have to be to lift a 2000 N car? GIVEN: WORK: Platform: F = 2000 N A = ? Plunger: F = 20 N A = 3 m2 2000 N = 20 N A1 3 m2 (2000 N)(3 m2) = (20 N)(A1) A1 = 300 m2

Bernoulli’s Principle As the velocity (speed) of a fluid increases, the pressure of the fluid decreases.

Bernoulli’s Principle Airplane wings are designed so air (a fluid!) flows more quickly over the top of the wing. The higher speed causes lower pressure above the wing. Underneath the wing, air pressure is higher… this helps lift the airplane up. Airplane Lift

You try it! Based on Bernoulli’s principle, what should happen when air is blown through the straw under the paper bridge?

Try these too!

Review An object weighing 56 N displaces 89 N of water. Will it sink or float? A 50 N object displaces 200 mL of water weighing 1.96 N. Draw a diagram illustrating the opposing forces on the object. Will it sink or float? A mechanic exerts 10 N of force on a 0.8 m2 piston. How much force can the large piston (area = 23 m2) support? You exert 17 N of force on the 2 m2 input piston of a hydraulic device. What must be the area of the large piston to lift 70 N?

Review Archimedes’ Principle problems: Buoyant force vs. Weight Will objects sink or float? An object weighing 33 N displaces 72 N of water. Will it sink or float? A 50 N object displaces 200 mL of water weighing 1.96 N. Draw a diagram illustrating the opposing forces on the object. Will it sink or float? An object weighing 23 N is dropped into an overflow can. The displaced water is collected in a 40 N beaker. If the weight of the beaker full of water is 61 N, did this object sink or float?

Review Pascal’s Principle Problems A hydraulic hospital bed requires 10 N of force to be exerted on a 0.5 m2 piston. If the area of the bed is 5 m2, what is the maximum weight for a patient it can lift? A mechanic needs to lift a 5000 N truck. If he exerts a 30 N force on a 1 m2 piston, what must be the area of the platform the truck sits on?

Pascal’s Practice A mechanic exerts 10 N of force on a 0.8 m2 piston. How much force can the large piston (area = 23 m2) support? You exert 17 N of force on the 2 m2 input piston of a hydraulic device. What must be the area of the large piston to lift 70 N? A hydraulic lift has a 3000 N car on the 40 m2 large piston. How much force needs to be exerted on the small piston (area= 5 m2)?

Review Matching: Kinetic Theory of Matter Law of Conservation of Mass Law of Conservation of Energy Buoyant force Archimedes’ Principle Viscosity Pascal’s Principle