A cylindrical tank, 3 m in diameter, holds water to a depth 64 cm. If water is drained through a pipe of diameter d mm at a speed of 150 m/min, it takes 2.5 hours to empty the tank.
(a) Find the value of d.
(b) Find the time saved in emptying the tank if d=20 and the water is drained through the pipe at a speed of 160 m/min.
Thank you!!
A maths question
2007-05-25 4:16 am
回答 (3)
2007-05-25 4:49 am
✔ 最佳答案
a)係要小心d單位者
同知道圓柱體體積既公式 V = pi r^2 h
r 係半徑, h 係高度
pi (3/2)^2 (64/100) = pi (d/2000)^2 * 150 * (2.5 * 60)
simply, d = 16
b)
let t be new time used in emptying the tank in minutes
pi (3/2)^2 (64/100) = pi (20/2000)^2 * 160 * t
simply,
t = 90 min = 1.5 hrs
time saved in emptying the tank
= 2.5 - 1.5
= 1 hr
2007-05-25 4:49 am
a)
volume of water in the tank = 3.14x(1.5^2) x 0.64 m^3
speed of water draining out = 3.14x[(d/2)^2] x 150 m^3/min
3.14x[(d/2)^2] x 150 x 2.5 x 60 = 3.14x(1.5^2) x 0.64
d = 0.016 m = 16mm
b)
Time required this time = 2.5 / [(20/16)^2 x 160/150] = 1.5 hours
Time saved = 2.5-1.5 = 1 hour
volume of water in the tank = 3.14x(1.5^2) x 0.64 m^3
speed of water draining out = 3.14x[(d/2)^2] x 150 m^3/min
3.14x[(d/2)^2] x 150 x 2.5 x 60 = 3.14x(1.5^2) x 0.64
d = 0.016 m = 16mm
b)
Time required this time = 2.5 / [(20/16)^2 x 160/150] = 1.5 hours
Time saved = 2.5-1.5 = 1 hour
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