Fluid Dynamics

FLUID MECHANICSMs. Arra C. Quitaneg

04/08/2023Prepared by: Ms. Paz Morales and Ms. Arra Quitaneg

Pressure

Which of the two exerts greater pressure?Why?

A. m= 100 g B. m= 200 g


Pressure

Which of the two exerts greater pressure? Why?

A. m= 100 g

B. m= 100 g


PRESSUREForce per unit area

When a fluid is at rest, it exerts a force perpendicular to any surface in contact with it.

The force exerted by the fluid is due to the molecules colliding with its surroundings.


Factors affecting PressureForce or Weight of the objectArea of support

Pressure = Force/ Area

Pressure is the ratio of the force to the area over which it is applied.

Unit: 1 Pascal (Pa) = 1 N/m204/08/2023

Prepared by: Ms. Paz Morales and Ms. Arra Quitaneg

Do you want to try this?



LIQUID PRESSURE


LIQUID PRESSUREF = AhgP = F/ A

Liquid pressure = gh=density of the liquidg= acceleration due to

gravityh= depth



Fluid Pressure Pressure:

Units of measure: pounds per square inch (psi), atmospheres (atm), or torr (which is a millimeter of mercury).

The S.I. unit for pressure is the pascal, which is a Newton per square meter: 1 Pa = 1 N / m 2. Atmospheric pressure is at sea level is normally:

1 atm = 1.01 ·10 5 Pa

= 760 torr = 14.7 psi.

At the deepest ocean trench the pressure is about 110 million Pascals.

Prepared by: Ms. Paz Morales and Ms. Arra Quitaneg04/08/2023

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Fluid pressureLiquid pressure Atmospheric pressureFluid pressure in liquid

varies with depth.

Due to the weight of the water column above the object submerged.

Due to the weight of the column of air above the surface.

Higher altitude – less atmospheric pressure


Which has greater liquid pressure?

Pressure does not depend on the amount of the liquid


Liquid Pressure


ATMOSPHERIC PRESSUREPressure of the Earth’s atmosphere.

1 atm = 1.013 x 105 Pa



Body moves from higher pressure to a lower pressure area.


Water distributionIf a water tower is only a storage device, why

is it so tall?


WATER DISTRIBUTIONWater accelerates only if pressure is out of

balance.

The deeper the water, the more weight there is overhead and the greater the pressure.

Water will not flow if there is no difference in pressure.


Next time you take a shower…Oh! Thanks to the difference

in pressure that I am able

to take a shower! Physics

works !!!!


Think about these…Consider an air –filled balloon weighted so

that it is on the limit of sinking. That its over all density just equals that of water. Now, if you push it beneath the surface, it will

a) Sinkb) Return to the surfacec) Stay at the dept to which it is pushedExplain your answer


Farm silos have bands around them to provide sturdiness to the walls. Why are the bands closer together near the bottom of the silo than on top?


Explain how level hose works.


Diver Jeff designs a new scuba setup that is so profoundly simple he is surprised that no one has thought of this before. He has attached one end of a long garden hose to a large Styrofoam to keep the hose above the water level. He will breathe through the other end of the hose as he explores the depths. What is wrong with his simple design?


Sample Problem:

Natsci 24: Topic 1 (Hydrostatics)DLS-CSB-SMS-NATSCI AREA


Solution:

Thus, the equivalent force is 240 N.

Problem 1:

A child wants to pump up a bicycle tire so that its pressure

is 2.5 x 105 Pa above that of atmospheric pressure. If the child uses a pump with a circular piston 0.035 m in diameter, what force must the child exert?


AFP PAF

NF 240

25 )2035.0)()(105.2( xF

04/08/2023

Sample Problem:



Problem 2:

In a classroom demonstration, a 73.5-kg physics professor lies on a “bed of nails.” The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board. While the professor is lying down, approximately 1900 nails make contact with his body. What is the average force exerted by each nail on the professor’s body?


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Sample Problem:



Problem 2:

In a classroom demonstration, a 73.5-kg physics professor lies on a “bed of nails.” The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board. While the professor is lying down, approximately 1900 nails make contact with his body. What is the average force exerted by each nail on the professor’s body?

Solution:

This gives about 0.379 N


AFP

NF 379.0

nailsS

mkgF

1900

)8.9)(5.73( 2

Amg

AWP

04/08/2023

Sample Problem:



Problem 3:

A swimming pool has the dimensions 15.0 m x 20.0 m. It is filled with water to a uniform depth of 8.00 m. The

density of water = 1.00 × 103 kg/m3.


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Sample Problem:



Solution:

Thus, the equivalent pressure is 1.8 x 105 Pa

Problem 3:

A swimming pool has the dimensions 15.0 m x 20.0 m. It is filled with water to a uniform depth of 8.00 m. The density of water = 1.00 × 103 kg/m3. What is the total pressure exerted on the bottom of the swimming pool?


ghP

PaxP 5108.1

)8.9)(8)(100.1( 333

smm

mkgxP

04/08/2023

AssignmentBring the following by group: 2 identical drinking glasses 2 straws 1 pin ½ crosswise short bond paper 2 pingpong balls 1 yard length of a string Adhesive tape 2 empty aluminum cans (identical) hair dryer


AssignmentClayAluminum foilCoinsbasin


Problem-solving:The surface of the

water in a storage tank is 30 m above a water faucet in the kitchen of a house, calculate the water pressure at the faucet.


Pressure

Pressure04/08/2023


Estimate the pressure exerted on a floor by a) a 50 kg model standing momentarily on a single spiked heel (area = 0.05 cm2) and compare it b) to the pressure exerted by a 1500 kg elephant standing on one foot (area = 800 cm2).


Pascal’s principleBlaise Pascal

Pressure applied to a confined fluid increases the pressure throughout by the same amount.


Pascal’s principle

Any change in the pressure of an incompressible fluid is transmitted uniformly in all directions throughout the fluid.

Pressure is transferred undiminished in a fluid.

P P



Application: Hydraulic Jack

Changes in pressure are transmitted uniformly through a fluid and the pressure pushes outward in all directions.

FA

FA



oil

A2F1

A1

F2h1

h2


A piston of cross-sectional area "a" is used in a hydraulic press to exert a small force of magnitude "f" on the enclosed liquid. A connecting pipe leads to a larger piston of cross-sectional area A. If the piston diameters are 3.80 cm and 53.0 cm, what force magnitude on the small piston will balance a 20.0 kN force on the large piston?


Surface tensionTendency of the liquid

surface to contract.

Surface behaves as elastic film.

Caused by molecular attractions.

Soapy water has less surface tension than pure water.

Spherical water droplet

Water strider04/08/2023


Why don’t boats made of steel SINK?

Is it possible for a material that is MORE DENSE than water to float?


BUOYANCY04/08/2023


BuoyancyA body immersed in water seems to

weigh less than when it is in air.

Buoyant force- force exerted by liquid to an object immersed on it


Buoyant force


BUOYANT FORCEFB = F2 – F1

FB = g A (h2 – h1 )

FB = gV


Buoyant forceFB = gV

=density of the liquidg=acceleration due to gravity

V = volume of the object


BuoyancyAccordingly, if the weight of the displaced water equals the

weight of the object then it floats.

Buoyant force is now equal to the weight of the object.

This is known as the principle of flotation: A floating object displaces a weight of fluid equal

to its own weight.


Archimedes principleThe buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.


Floating of an objectObject floats if density of object is

less than the density of the fluid.

An object is in equilibrium if the net force is zero.

Buoyant force = Weight of the object


Fraction of the object submerged:


FLOATING RESTAURANTS


A 15.0 kg solid gold statue is being raised from a sunken ship. What is the tension in the hoisting cable when the statue is at rest. A) completely immersed b) out of water

Density of gold= 19.3 x 103 kg/m3

Density of air = 1.2 kg/m3

Density of seawater- 1.025 x 103 kg/m3


A wooden block of wood with a volume of 125 m3 floats on seawater. What fraction of object is submerged on seawater? Density of seawater- 1.025 x 103 kg/m3

Density of wood = 0.9 x 103 kg/m3


SeatworkA block of steel measuring 2m on each

side was accidentally dropped in seawater reaching a depth of 10 m. How much force is needed to lift the steel block if its density is 7.8 x 103 kg/m3 ?

Density of seawater- 1.025 x 103 kg/m3

A 0.5 kg block of wood is floating in water. What is the magnitude of the buoyant force acting on the block?


A 70 kg ancient statue lies at the bottom of the sea. Its volume is 3.0 x 104 cm3. How much force is needed to lift it?


A small piston with a diameter of 0.5 m is used in a hydraulic lift. The larger piston has a diameter of 2m, how much force is needed to lift a car weighing 10 000 N ?

How much pressure is felt by woman standing on a heel with an area of 0.025 cm 2 , if her mass is 55 kg?


The strongest aluminum boat!!!Prepare 144 in2

aluminum foil.

Make your own boat design using the cut aluminum foil.

Prepare for the battle.

Which boat design will support more coins?


POINTING SYSTEMNO . OF COINS POINTS

10 515 1020 1525 2030 2535 3040 35


Bernoulli’’s principle


Activities…….


Bernoulli’s PrincipleWhen the speed of the fluid increases, pressure in the fluid decreases.


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Bernoulli's Principle For Bernoulli's Principle to

apply, the fluid is assumed to have these qualities:◦ fluid flows smoothly

◦ fluid flows without any swirls (which are called "eddies")

◦ fluid flows everywhere through the pipe (which means there is no "flow separation")

◦ fluid has the same density everywhere (it is "incompressible" like water)


Bernoulli's PrincipleOnly true for a non-viscous fluid flowing

at a constant height. It follows directly from the Bernoulli equation:P + ½ v

2 + g y = constant.

If y is a constant, then P + ½ v

2 = constant.

This shows that if pressure increases, then speed decreases, and versa visa.


Airplane wing


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Bernoulli’s principle Applications

Atmospheric pressure decreases in a strong wind, tornado or hurricane.

Faster airLOWER PRESSURE

HIGHER PRESSURE


The curved shape of an umbrella can be disadvantageous on a windy day!


Think…think…think…

Roofs of houses are sometimes blown off (or are they pushed off?) during a storm. Explain using Bernoulli’s principle.

An unvented building with airtight closed windows is in more danger of losing its roof than a well vented building.


Children are told to avoid standing too close to a rapidly moving train because they might get sucked under it. Is it possible? Why?


House roofing


AssignmentWhich is the

best roof design to prevent roof destruction due to difference in pressure above and below the roof.


THANK YOU……


RemindersQuiz on MondayPart 1: Written examPart 2: Practical exam(floating restaurant

design)

Bring all the materials you need for the design. Research on the weights of the objects you want to place in your floating restaurant. Practice computation.


Education

Fluid Dynamics