UTPA STEM/CBI Courses/Physics (Calculus Based)/Fluid Mechanics

Course Title: Calculus Based Physics I

Lecture Topic: Fluid Mechanics

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design

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

Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
- Snowshoes, high heels, walking upright versus crawling, bed of nails: pressure (P = F/A)*
- Old-time 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

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

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
  - Self-reading 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 cross-sectional area of 3.00 cm2 and its large piston has a cross-sectional 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).

- - - (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 12.0-cm 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 cross-sectional are A = 2.50 x 10-5 m2, and the needle has a cross-sectional area a = 1.00 x 10-8 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.

OBJECTIVE

By the next class period, students will be able to:

The objectives will require that students be able to:

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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