This scenario shows a 0.1-m diameter pipe at A filling a tank that is 2.0 m long and 1.9 m wide. Water flowing at a constant rate fills the tank to a height of 3.8 m in 7 minutes. Determine the average velocity of the flow from the pipe at A. Show your answer to 3 significant figures with units of m/s.

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Explanation:

(a) For steady flow we have

Q1 + Q2 + Q3 = Q4, or Fig. P3.8

VA VA VA VA 11 2 2 33 4 4 + + = (1)

Since 0.2Q3 = 0.1Q4, and Q4 = (120 m3/h)(h/3600 s) = 0.0333 m3/s,

3

4

3

2 3

(0.0333 m /s) (b) 2 (0.06 ) 2

Q V Ans.

A π == = 5.89 m/s

Substituting into (1),

22 2

1 (0.04 ) (5) (0.05 ) (5.89) (0.06 ) 0.0333 (a) 44 4

V Ans. ⎛⎞ ⎛⎞ ⎛⎞ ππ π

⎜⎟ ⎜⎟ ⎜⎟ ++ = ⎝⎠ ⎝⎠ ⎝⎠ V 5.45 m/s 1 =

From mass conservation, Q4 = V4A4

3 2

4 (0.0333 m /s) V ( )(0.06 )/4 (c) = π

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