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3 years ago

7

Water flows into a swimming pool at the rate of 5.85 gal/min. If the pool dimensions are 21.2 ft wide, 46.1 ft long and 19.4 ft

deep, how long does it take to fill the pool? (1 gallon = 231 cubic inches) Answer in units of min.

1 answer:

Lana71 [14]3 years ago

6 0

First, calculate volume:

volume = 21.2 ft * 46.1 ft * 19.4 ft

volume = 18,960 ft^3

Convert to gallon:

volume = 18,960 ft^3 * (12 in / 1 ft)^3 * (1 gallon / 231 in^3)

volume = 141,830.71 gallon

Therefore the time is:

time = 141,830.71 gallon / (5.85 gal/min)

time = 24,244.57 min

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Let final Temperature be T

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specific heat of water $c=4.18 kJ/kg-K$

balancing energy

Heat lost by hot fluid=heat gained by cold Fluid

$\dot{m_c}c(T_h_i-T_h_e)= \dot{m_h}c(80-20)$

$2\times (160-T)=1.2\times (80-20)$

$160-T=36$

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As heat exchanger is counter flow therefore

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$LMTD=91.49^{\circ}C$

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$A=\pi DL=5.144$

$L=\frac{5.144}{\pi \times 0.015}$

$L=109.16 m$

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