Section 1.6: Problem-Solving Strategies (Fluids)
Here we outline systematic methods for solving fluid mechanics problems, such as pressure, buoyancy, and fluid dynamics. These strategies help structure your approach so you don’t miss critical steps.
Step-by-Step Approach:
- Draw a clear diagram of the situation.
- List all known quantities and what is being asked.
- Identify the relevant physics principles (e.g., Bernoulli, Archimedes, Continuity).
- Write down the fundamental equations.
- Substitute known values, keep track of units.
- Solve algebraically, then numerically.
- Check units and physical reasonableness of your answer.
Example
A rectangular block (volume = 0.01 m³, mass = 8 kg) is placed in water. Will it float or sink? If it floats, what fraction is submerged?
Buoyant force: \( F_b = \rho_{water} V g = 1000 \cdot 0.01 \cdot 9.8 = 98 \,\text{N} \)
Weight of block: \( W = mg = 8 \cdot 9.8 = 78.4 \,\text{N} \)
Since \( F_b > W \), the block floats. Fraction submerged: \( \frac{W}{F_b} = \frac{78.4}{98} \approx 0.8 \) or 80%.
Practice Problems
- List the first three steps you would take to solve a buoyancy problem.
- Explain how to decide when to apply Bernoulli’s equation vs. hydrostatics.
- Why is drawing a diagram essential in pressure and force problems?
- A boat weighs 5000 N. What volume of water must it displace to float?
- What strategy would you use to solve a problem involving fluid flow in pipes of different diameters?