A constant-area tank has A=2.20 m^2. The initial height is h0=0.35 m and the final height is h=0.60 m. The inlet flow rate is Qin=15.5 L/min and the outlet flow rate is Qout=6.5 L/min. How long does it take to reach the final height?单项选择题
A
48 min
B
61 min
C
72 min
D
92 min

Question

A constant-area tank has A=2.20 m^2. The initial height is h0=0.35 m and the final height is h=0.60 m. The inlet flow rate is Qin=15.5 L/min and the outlet flow rate is Qout=6.5 L/min. How long does it take to reach the final height?单项选择题

A

48 min

B

61 min

C

72 min

D

92 min

BlackTom AI · Accepted Answer

A dh/dt balance for a tank with constant cross-sectional area gives A dh/dt = Qin − Qout. Integrating for a constant net flow yields t = A (h − h0) / (Qin − Qout).

Step-by-step with unit conversions and intermediate steps:
1. Height change: Δh = h − h0 = 0.60 − 0.35 = 0.25 m.
2. Volume change: ΔV = A · Δh = 2.20 m^2 · 0.25 m = 0.55 m^3.
   (Also expressible in liters: 0.55 m^3 · 1000 L/m^3 = 550 L.)
3. Convert flow rates to consistent units (either m^3/min or L/min).
   - Qin = 15.5 L/min = 0.0155 m^3/min.
   - Qout = 6.5 L/min = 0.0065 m^3/min.
   - Net flow = Qin − Qout = 0.0155 − 0.0065 = 0.0090 m^3/min (or 9.0 L/min).
4. Time required: t = ΔV / (Qin − Qout) = 0.55 m^3 / 0.0090 m^3/min = 61.111... min.
   (Using liters: t = 550 L / 9.0 L/min = 61.111... min.)

Why the correct answer is correct:
The net inflow is 9.0 L/min, so filling 550 L at that net rate takes 550/9 ≈ 61.11 minutes. Rounding to the nearest whole minute gives 61 min.

Why the other choices are incorrect:
- 48 min would imply a net inflow ≈550/48 ≈11.46 L/min, larger than the actual 9.0 L/min.
- 72 min would imply net inflow ≈550/72 ≈7.64 L/min, smaller than actual.
- 92 min would imply net inflow ≈550/92 ≈5.98 L/min, much smaller than actual.
Only 61 min matches the computed net fill time.

Final answer: 61 min (matches the provided correct answer).

A constant-area tank has A=2.20 m^2. The initial height is h0=0.35 m and the final height is h=0.60 m. The inlet flow rate is Qin=15.5 L/min and the outlet flow rate is Qout=6.5 L/min. How long does it take to reach the final height?单项选择题

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A constant-area tank has A=2.20 m^2. The initial height is h0​=0.35 m and the final height is h=0.60 m. The inlet flow rate is Qin​=15.5 L/min and the outlet flow rate is Qout​=6.5 L/min. How long does it take to reach the final height?单项选择题

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The presence of fuel stains around a fuel nozzle would indicate

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A 3/8 inch aircraft high pressure flexible hose as compared to 3/8 inch metal tubing used in the same system will

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更多留学生实用工具

希望你的学习变得更简单

A constant-area tank has A=2.20 m^2. The initial height is h0=0.35 m and the final height is h=0.60 m. The inlet flow rate is Qin=15.5 L/min and the outlet flow rate is Qout=6.5 L/min. How long does it take to reach the final height?单项选择题