UTPA STEM/CBI Courses/Physics (Calculus Based)/Fluid Mechanics
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Course Title: Calculus Based Physics I
Lecture Topic: Fluid Mechanics
Instructor: Liang Zeng
Institution: University of TexasPan American
Backwards Design[edit]
Course Objectives
 Primary Objectives By the next class period students will be able to:
 Review pressure (P = F/A) – atmospheric pressure, barometer, manometer
 Know that the term “fluid” includes liquids and gases
 Know Pascal’s Law (pressure is transmittable in fluids) and its applications
 Know that pressure increases with depth in fluids (the higher above earth’s surface the lower the pressure, the deeper below the water the greater the pressure) and how to calculate the pressure
 Know how to calculate buoyant force on an object partially or fully submerged in a fluid; Archimedes principle
 Know that Av = constant for steady flow rate (volume flux, units of m3/s) through a pipe (so A1v1 = A2v2)
 Know that the pressure of a fluid decreases as the speed of the fluid increases (Bernoulli) – airplane wings, perfume bottle
 Sub Objectives The objectives will require that students be able to:
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 Difficulties Students may have difficulty:
 Confusion between ρfluid and ρobject when doing calculations involving buoyant objects
 Confusion between volume of fluid displaced (submerged portion of object) and volume of the entire object
 Confusion about the point of reference (height versus depth) in the formula P = ρgh
 RealWorld Contexts There are many ways that students can use this material in the realworld, such as:
 Snowshoes, high heels, walking upright versus crawling, bed of nails: pressure (P = F/A)*
 Oldtime perfume bottle (Figure 14.23 page 406 Serway), airplane wing and upthrust: Bernoulli’s law*
 Car brakes, hydraulic lift: Pascal’s law*
 Three Gorges/Yangzi River, thumb over garden hose: equation of continuity*
 Iceberg, boat, hot air balloon, floatation devices: buoyancy*
Model of Knowledge
 Concept Map
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 Content Priorities
 Enduring Understanding
 Calculating pressure (P = F/A) – atmospheric pressure, barometer, manometer
 The term “fluid” includes liquids and gases
 Pascal’s Law (pressure is transmittable in fluids) and its applications
 Pressure increases with depth in fluids (the higher above earth’s surface the lower the pressure, the deeper below the water the greater the pressure) and how to calculate the pressure
 Calculating buoyant force on an object partially or fully submerged in a fluid
 Av = constant for steady flow rate (volume flux, units of m3/s) through a pipe (so A1v1 = A2v2)
 Important to Do and Know
 The pressure of a fluid decreases as the speed of the fluid increases (Bernoulli) – airplane wings, perfume bottle
 Worth Being Familiar with
 Calculations using Bernoulli’s equation
 Enduring Understanding
Assessment of Learning
 Formative Assessment
 In Class (groups)
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 Homework (individual)
 Pay attention to the following new units: Pa (N/m2), m3, L, kg/m3
 Selfreading Chapter 14 in the textbook
 (Calculating pressure using P = F/A, Serway 7th edition #3 page 408). A 50.0 kg woman balances on one heel of a pair of high heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor?
 (Pascal’s Law (pressure is transmittable in fluids) and its applications: Hydraulic lift, Serway 7th edition #8 page 409). The small piston of a hydraulic lift has a crosssectional area of 3.00 cm2 and its large piston has a crosssectional area of 200 cm2 (figure 14.4a). What force must be applied to the small piston for the lift to raise a load of 15.0 kN? (In service stations, this force is usually exerted by air).
 In Class (groups)



 (Pressure varies with depth in fluids: Swimming pool no torque, Serway 7th edition #11 page 409). A swimming pool has dimensions 30.0 m x 10.0 m and a flat bottom. When the pool is filled to a depth of 2.00 m with fresh water, what is the force caused by the water on the bottom? On each end? On each side?
 (Calculating buoyant force on an object: Fully submerged, Serway 7th edition #23 page 411). A 10.0 kg block of metal measuring 12.0 cm x 10.0 cm x 10.0 cm is suspended from a scale immersed in water as shown in Figure P14.22b. The 12.0cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water.
 What are the forces acting on the top and bottom of the block? (Take P0 = 101.30 kPa.)
 What is the reading of the spring scale?
 Show that the buoyant force equals the difference between the forces at the top and bottom of the block?





 (Calculating buoyant force on an object: Partially submerged, Serway 7th edition #27 page 411). A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water.
 What is the distance from the horizontal top surface of the cube to the water level?
 What mass of lead should be placed on the cube so that the top of the cube will be just level with the water?
 (Flow rate through a pipe is constant (A1v1 = A2v2): hypodermic syringe, Serway 7th edition #49 page 413). A hypodermic syringe contains a medicine having the density of water (Fig. P114.49). The barrel of the syringe has a crosssectional are A = 2.50 x 105 m2, and the needle has a crosssectional area a = 1.00 x 108 m2. In the absence of a force on the plunger, the pressure everywhere is 1 atm. A force F ⃗ of magnitude 2.00 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needles tip.
 (Calculating buoyant force on an object: Partially submerged, Serway 7th edition #27 page 411). A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3 floats on water.


 Summative Assessment
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Legacy Cycle[edit]
OBJECTIVE
By the next class period, students will be able to:
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The objectives will require that students be able to:
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THE CHALLENGE
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GENERATE IDEAS
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MULTIPLE PERSPECTIVES
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RESEARCH & REVISE
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TEST YOUR METTLE
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GO PUBLIC
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PreLesson Quiz[edit]
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Test Your Mettle Quiz[edit]
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