Day13

Physics131

Density and Pressure

• = Mass/Volume, kg/m2 density • P, Pressure defined as F/A, N/m2, Pascals, Pa• Atmospheric pressure approx. 1.0 x 105 Pa.

Atmospheric Pressure and Gauge Pressure

• Absolute – total of atmospheric + gauge• Gauge is pressure “above” atmospheric

pressure. Sure enough, it’s what you read on a gauge!

Car Tires

• The four tires of an automobile at inflated to a gauge pressure of 2.0 x 105 Pa. Each tire has an area of 0.024 m2 in contact with the ground.

• ? Determine the weight of the automobile ??

Variation of Pressure with Depth

• As you go deeper and deeper in a liquid, the density stays (just about) constant, but the pressure increases.

• P = Po + gh

“Deception Point” by Dan Brown

• Mariana Trench is seven miles deep.• Water Pressure at the bottom 18 thousand

pounds.• ? Is this reasonable ?

“The Whale” or Moby Dick, page 336

• “Owing to the enormous surface of him – in a full grown sperm what something less than 2000 square feet – the pressure of the water is immense. We all know that an astonishing atmospheric weight we ourselves stand up under, even here, above ground, in the air, how fast then the burden of a whale, bearing on his back a column of two hundred fathoms of ocean! It must be equal to the weight of fifty atmospheres.”

Concrete Column

• Given: 1.0 m3 of concrete weighs 5.0 x 104 N• The compression strength of concrete (the

maximum pressure than can be exerted on the base of the structure) is 1.7 x 107 Pa.

• ? What is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight ?

Pascal’s Principle

• P1 = P2

• or F1/A1 = F2/A2

• Hydraulic lift for car repair• Brakes (and perhaps clutch) on your car

Auto Lift

• An hydraulic automobile lift has pistons of 8.00 cm and 36.0 cm diameters.

• Finput = 825 N

• ? What weight can this device lift ?

Archimedes’ Principle

• An object completely or partially submerged in a fluid is buoyed up by a force with magnitude equal to the weight of the fluid displaced by the object.

• = fluid Vfluid g

The Five Blocks

Bowling Ball

• Will this bowling ball float?• ? Why ?

• Extra Credit HW Problem for tomorrow or Thursday.

Spanish Submarine

• Spain has a submarine under construction which may not float!

• https://www.youtube.com/watch?v=SMojo9zKrIM

Iceberg

• Suppose that the part of an iceberg that extends above the water were suddenly removed. If this occurred, which of the following is correct ? The

• A. center of mass of the iceberg would sink slightly.

• B. buoyant force on the iceberg would decrease• C. density of the iceberg would slightly decrease• D. pressure at the bottom of the iceberg would

increase.

Tethered Balloon

• Balloon mass = 0.0120 kg• HE = 0.181 kg/m3

• Rballoon = 0.500 m

• ? What fluid is being displaced? • ? What’s the tension on the string tying the

balloon down ?

“Danny Deckchair”

• Danny attaches helium-filled balloons to his deckchair and soars off into the night.

• Danny’s mass = 80.0 kg.• Mass of the chair = 2.00 kg• Each balloon has mass = 0.444 kg (deflated)• air = 1.290 kg/m3

• HE 0.179 kg/m3

• Volume of each inflated balloon = 4/3 r3 = 4m3

• ? How many balloons are required?

Wi-Fi Balloon Experiment

Project Loon seeks to use a global network of high-altitude balloons to connect people in rural and remote areas who have no internet at all.http://www.google.com/loon

Equation of Continuity

• A1v1 = A2v2

• So if the tube gets smaller, the flow must speed up.

Fluid Flow and Continuity

• The Garfield Thomas water tunnel at Penn State U. has a circular cross section that constricts from a diameter of 3.6 m to the test section, which is 1.2 m in diameter.

• ? If the speed of the flow is 3.00 m/s in the larger-diameter pipe, determine the speed of flow in the test section. ?

Bernoulli’s Equation

• P + ½ v2 + g y = constant

• You are driving in a convertible car with the top up and the windows closed. You note that the fabric top puffs. To explain this interesting phenomenon, it is easiest to invoke

• (a) Bernoulli’s principle• (b) Newton’s laws• (c) both

Little Dutch Boy

• Walking home from school one day, a youngster in the Netherlands discovers a hole in the levee which holds back the sea.

• The hole is 1.20 cm diameter and 2.00 m below the surface of the water.

• water = 1.03 x 103 kg/m3

• ? What’s the force on his finger ?• ? How long, T, for 1234 m3 of water to flow ?

Torricelli• Evangelista Torricelli served as Galileo’s secretary from

1641-1642 and succeeded him as the court mathematician to Grand Duke Ferdinando II of Tuscany. He lived in the ducal palace in Florence from then until his death.

• Torricelli was the first person to create a sustained vacuum and to discover the principle of a barometer. In 1643 Torricelli proposed an experiment, later performed by his colleague, Vincenzo Viviani, that demonstrated that atmospheric pressure determines the height to which a fluid will rise in a tube inverted over the same liquid. This concept led to the development of the barometer.

• A unit of pressure, “torr”, was named for him. • 760 torr = 760 mm of mercury = 1 atmosphere.

Torricelli’s Law

• Given: A container with some fluid inside.• If a hole is poked in the container at a depth h

below the surface of the fluid, the fluid exits with the speed v = (2gh)1/2.

• Home plumbing example

Coanda Effect

• The Coanda Effect is the tendency of a fluid jet to be attracted to a nearby surface.

• One Asheville example is at the Bier Garden• Another in Asheville is the large, round fountain

in Pack Square• Yet another are gutter covers from various

manufacturers. Water doesn’t “let go” until the force of gravity is stronger than the force from the Coanda effect.

Find the Error, orCorrect the Prose