Qualitative/quantitative translation (QQT)
Water columns over a narrowing pipe
- Unit 8
- 8 points
- About 18 minutes
You can use a calculator on this question, just like on exam day.
A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator allowed. The CED suggests 15–20 minutes.
The question
Water flows steadily to the right through a horizontal pipe that narrows from cross-sectional area A₁ in the wide section to A₂ = A₁/3 in the narrow section. A thin vertical tube, open at the top, is attached to the top of each section, and water rises in each tube to a height that indicates the pressure in the pipe below it. Treat the water as an ideal fluid (incompressible, no viscosity), and the pipe is completely full. Use g = 9.8 m/s² (answers that use g = 10 m/s² are also accepted).
Suggested time: 18 minutes
Your answers are saved in this browser as you type.
Part (a)
3 pointsIn which vertical tube does the water rise higher: the one above the wide section, the one above the narrow section, or neither (equal heights)? Justify your answer. Do not use equations in this part; reason in words.
0 / 2,500 characters
Part (b)
3 pointsLet v₁ be the speed of the water in the wide section. Derive an expression for the difference Δh between the water heights in the two tubes, in terms of v₁ and g.
0 / 2,500 characters
Part (c)
2 points(i) Explain how your expression from part (b) agrees with your answer to part (a). (ii) The flow is adjusted so that v₁ doubles. Use your expression to predict how Δh changes.
0 / 2,500 characters
Checking scoring…
Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.