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Unit notes and practice questions

Grade 12 Physics unit 3: Fluid Mechanics

Everything here is for unit 3 of the Grade 12 Physics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.

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5
Cards
10
Practice questions on unit 3
69–117
The textbook pages for unit 3

What unit 3 covers

  1. 1.Fluid Statics
  2. 2.Pressure in fluids at rest
  3. 3.Archimedes' principle
  4. 4.Fluid flow
  5. 5.Safety and high pressure

Short notes for unit 3

The cards filed under this chapter on the Grade 12 Physics page. Open one at a time.

Pabs=Patm+PgageP_{\text{abs}} = P_{\text{atm}} + P_{\text{gage}}
PabsP_{\text{abs}}
absolute pressurePaPa
PatmP_{\text{atm}}
local atmospheric pressurePaPa
PgageP_{\text{gage}}
gauge pressurePaPa

When you use it

Use to convert between pressure gauge readings and the true absolute pressure relative to complete vacuum.

Watch out

Pressure measuring gauges read zero at atmospheric pressure. Never substitute gauge pressure directly into the ideal gas equation without adding atmospheric pressure.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

FB=ρfluidgVdispF_B = \rho_{\text{fluid}} g V_{\text{disp}}
FBF_B
buoyant forceNN
ρfluid\rho_{\text{fluid}}
density of the surrounding fluidkg m−3kg\,m^{-3}
gg
acceleration due to gravitym s−2m\,s^{-2}
VdispV_{\text{disp}}
volume of fluid displacedm3m^3

When you use it

Use to determine the upward buoyant force acting on any partially or completely submerged object in a fluid.

Watch out

Use the density of the fluid, not the density of the object, to calculate the buoyant force.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

VdispVobj=ρobjρfluid\frac{V_{\text{disp}}}{V_{\text{obj}}} = \frac{\rho_{\text{obj}}}{\rho_{\text{fluid}}}
VdispV_{\text{disp}}
volume submerged in fluidm3m^3
VobjV_{\text{obj}}
total volume of the objectm3m^3
ρobj\rho_{\text{obj}}
density of the floating objectkg m−3kg\,m^{-3}
ρfluid\rho_{\text{fluid}}
density of the fluidkg m−3kg\,m^{-3}

When you use it

Use to calculate the fraction or percentage of a floating object submerged beneath the surface of a fluid.

Watch out

This equation applies only to floating objects in static equilibrium, where the object density is less than the fluid density.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

F1A1=F2A2\frac{F_1}{A_1} = \frac{F_2}{A_2}
F1F_1
force applied on input pistonNN
A1A_1
cross-sectional area of input pistonm2m^2
F2F_2
force exerted on output pistonNN
A2A_2
cross-sectional area of output pistonm2m^2

When you use it

Use when finding the force or piston area in hydraulic lifts, brakes, and presses where confined fluid transmits pressure equally.

Watch out

Make sure the areas A_1 and A_2 are in the same units before calculating. If diameters are given, use area proportional to diameter squared.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

P=P0+ρghP = P_0 + \rho g h
PP
absolute pressure at depth hPaPa
P0P_0
pressure at the fluid surfacePaPa
ρ\rho
density of the fluidkg m−3kg\,m^{-3}
gg
acceleration due to gravitym s−2m\,s^{-2}
hh
depth below the surfacemm

When you use it

Use to calculate total hydrostatic pressure at any depth below the open surface of a static liquid.

Watch out

Always add atmospheric pressure P_0 when asked for absolute pressure. If only gauge pressure is required, omit P_0.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

Practice questions on unit 3

10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.

Question 1

What is the SI unit of pressure?

  1. A.Pascal (Pa)
  2. B.Atmosphere (atm)
  3. C.Millimeter of mercury (mmHg)
  4. D.Pounds per square inch (psi)
Show the answer and why

Answer: A Pascal (Pa)

Why

In the SI system, pressure is measured in newtons per square meter (N/m2), which is defined as the pascal (Pa).

Question 2

For a fluid at rest in fluid statics, what is the value of the shear (tangential) stress?

  1. A.It is equal to atmospheric pressure
  2. B.It is zero
  3. C.It increases with fluid depth
  4. D.It equals the normal stress
Show the answer and why

Answer: B It is zero

Why

In a fluid at rest, there is no relative motion between adjacent fluid layers. Therefore, the shear stress is zero, and the only existing stress is the normal stress (pressure).

Question 3

According to Pascal's principle, what happens when an external pressure is applied to an enclosed static fluid?

  1. A.The pressure decreases with distance from the source
  2. B.The pressure change is transmitted undiminished to every point in the fluid
  3. C.The pressure increases only at the bottom surface
  4. D.The fluid becomes compressed to half its volume
Show the answer and why

Answer: B The pressure change is transmitted undiminished to every point in the fluid

Why

Pascal's principle states that a change in pressure applied to a static enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of its container.

Question 4

According to Archimedes' principle, the upward buoyant force acting on an object placed in a fluid equals the:

  1. A.Weight of the fluid displaced by the object
  2. B.Total weight of the object
  3. C.Surface area of the object
  4. D.Atmospheric pressure acting on the fluid surface
Show the answer and why

Answer: A Weight of the fluid displaced by the object

Why

Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces (FB = Wfluid).

Question 5

A mechanic in Addis Ababa measures the tire gauge pressure of a minibus to be 32.0 psi. If the local atmospheric pressure is 14.3 psi, what is the absolute pressure inside the tire?

  1. A.17.7 psi
  2. B.32.0 psi
  3. C.46.3 psi
  4. D.457.6 psi
Show the answer and why

Answer: C 46.3 psi

Why

Absolute pressure is found by adding atmospheric pressure to gauge pressure: Pabs = Patm + Pgage = 14.3 psi + 32.0 psi = 46.3 psi.

Question 6

A hydraulic press in a garage in Hawassa has a small piston with an area of 0.0020 m2 and a large piston with an area of 0.20 m2. If a total downward force of 18,000 N acts on the large piston, what minimum force must be applied to the small piston to lift the load?

  1. A.180 N
  2. B.360 N
  3. C.1,800 N
  4. D.90 N
Show the answer and why

Answer: A 180 N

Why

From Pascal's principle, F1 = (A1 / A2) × F2 = (0.0020 m2 / 0.20 m2) × 18,000 N = 0.01 × 18,000 N = 180 N.

Question 7

What is the gauge pressure in water at a depth of 25.0 m? (Take the density of water as 1.00 × 103 kg/m3 and g = 9.8 m/s2).

  1. A.2.45 &times; 10<sup>5</sup> Pa
  2. B.2.50 &times; 10<sup>4</sup> Pa
  3. C.3.46 &times; 10<sup>5</sup> Pa
  4. D.1.01 &times; 10<sup>5</sup> Pa
Show the answer and why

Answer: A 2.45 &times; 10<sup>5</sup> Pa

Why

The gauge pressure due to depth is P = ρgh = (1.00 × 103 kg/m3)(9.8 m/s2)(25.0 m) = 245,000 Pa = 2.45 × 105 Pa.

Question 8

Why does atmospheric pressure decrease as a person climbs to higher altitudes on a mountain?

  1. A.Gas particles move faster at higher altitudes
  2. B.The depth and density of the air column above both decrease
  3. C.Gravity stops acting on gas molecules at high elevation
  4. D.Water vapor disappears completely from the atmosphere
Show the answer and why

Answer: B The depth and density of the air column above both decrease

Why

Atmospheric pressure is caused by the weight of the air column above. At higher altitudes, there is less depth of atmosphere above you and the air is less dense, so the atmospheric pressure decreases.

Question 9

A rectangular wooden block floats in Lake Tana with 75% of its total volume submerged in fresh water (ρ = 1000 kg/m3). What is the density of the wooden block?

  1. A.250 kg/m<sup>3</sup>
  2. B.750 kg/m<sup>3</sup>
  3. C.1333 kg/m<sup>3</sup>
  4. D.75 kg/m<sup>3</sup>
Show the answer and why

Answer: B 750 kg/m<sup>3</sup>

Why

For a floating object, Vdisp / Vobj = ρobj / ρfluid. Therefore, ρobj = 0.75 × 1000 kg/m3 = 750 kg/m3.

Question 10

An open-end manometer is connected to a gas container. The fluid has a density of 850 kg/m3, and the liquid column in the open arm is 0.55 m higher than the arm connected to the gas. If atmospheric pressure is 96.0 kPa and g = 9.81 m/s2, what is the absolute pressure of the gas?

  1. A.91.4 kPa
  2. B.96.0 kPa
  3. C.100.6 kPa
  4. D.105.2 kPa
Show the answer and why

Answer: C 100.6 kPa

Why

When the open arm is higher, Pgas = Patm + ρgh. First, ρgh = (850 kg/m3)(9.81 m/s2)(0.55 m) = 4586 Pa = 4.6 kPa. Thus, Pgas = 96.0 kPa + 4.6 kPa = 100.6 kPa.

The app holds 12 questions on this unit, marked as you go. These are the first 10.

The textbook pages for unit 3

Unit 3 runs from page 69 to page 117 of the Ministry of Education edition.

Ministry of Education edition, English, 186 pages

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