Section 1.5: Applications of Fluids

This section applies the concepts of pressure, buoyancy, and fluid dynamics to real-world systems like hydraulic machines, airplanes, blood flow, and weather phenomena.

Key Applications:
  • Hydraulic Lift: Uses Pascal’s principle to amplify force.
  • Venturi Effect: Narrow pipes increase velocity, decrease pressure (used in carburetors & atomizers).
  • Airplane Wings: Bernoulli’s principle explains lift due to pressure difference above/below wing.
  • Blood Flow: Poiseuille’s law governs flow rate in arteries and veins.
  • Weather Systems: Pressure differences create wind and circulation.

Example 1

A hydraulic lift has piston areas \( A_1 = 0.01 \,\text{m}^2 \) and \( A_2 = 0.5 \,\text{m}^2 \). If a force of 200 N is applied to the small piston, find the load the large piston can lift.

Pascal’s principle: \( \frac{F_1}{A_1} = \frac{F_2}{A_2} \)

\( \frac{200}{0.01} = \frac{F_2}{0.5} \)

\( 20{,}000 = \frac{F_2}{0.5} \Rightarrow F_2 = 10{,}000 \,\text{N} \)

Example 2

A Venturi tube has diameters 10 cm and 5 cm. Water enters at 2 m/s at the wide section. Find the speed at the narrow section.

Continuity: \( A_1 v_1 = A_2 v_2 \)

Area ratio: \( A_1 = \pi (0.05)^2 = 0.00785 \,\text{m}^2 \), \( A_2 = \pi (0.025)^2 = 0.00196 \,\text{m}^2 \)

\( v_2 = \frac{A_1}{A_2} v_1 = \frac{0.00785}{0.00196} \times 2 \approx 8.0 \,\text{m/s} \)

Practice Problems

  1. A hydraulic lift has \( A_1 = 0.02 \,\text{m}^2 \) and \( A_2 = 0.4 \,\text{m}^2 \). Find the force needed to lift 4000 N.
  2. Explain how perfume atomizers use the Venturi effect to spray liquid.
  3. An airplane wing has air moving at 60 m/s above and 50 m/s below. If \( \rho = 1.2 \,\text{kg/m}^3 \), find the pressure difference.
  4. Why does blood pressure drop in smaller capillaries, even though velocity increases?
  5. Using Poiseuille’s law, explain why arteries with plaque buildup restrict blood flow.
  6. A weather map shows a low-pressure system. Explain why air flows toward it.
  7. A hydraulic press has a mechanical advantage of 25. If input force = 400 N, what is the output force?
  8. Water flows through a pipe narrowing to half its diameter. By what factor does velocity increase?
  9. Discuss why airplanes can still fly upside down despite Bernoulli’s principle.
  10. Describe one medical device that uses fluid principles (e.g., IV drip, blood pressure cuff).
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