The speed v of a liquid in a tube depends on the change in pressure ΔP and the density ρ of the liquid. The speed is given by the equation. v=k (ΔP/ρ) Where k is a constant that has no units. What is the value of n?
Correct answer: A. 1/2
- A. 1/2
- B. 1
- C. 3/2
- D. 2
Explanation
The correct answer is 1/2. Using dimensional analysis, the speed v (dimension [L][T]^-1) must be proportional to the square root of the pressure difference ΔP (dimension [M][L]^-1[T]^-2) divided by the density ρ (dimension [M][L]^-3). Thus, v = k(ΔP/ρ)^1/2 ensures that the dimensions on both sides of the equation match, confirming that n = 1/2. Other options do not satisfy the dimensional consistency and therefore are incorrect.
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