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A conical tank extends from two foot in diameter at the discharge to twelve feet in...

A conical tank extends from two foot in diameter at the discharge to twelve feet in diameter at the top with sides 30 degree from the vertical. Water flows into the tank at 100 lbm/min. How long does it take to fil the tank to 80 percent full?

Solutions

Expert Solution

The figure of cone is shown as:

The height of this figure is unknown which can be obtained the the concept of Trigonometory

Consider the following figure

In small triangle we have

tan30 = 2/h

h=2 ft

In big triangle

tan(30)=12/(h+H)

1/= 12/(2+H)

solving it we get H=4 ft

Now volume of the cone= (1/3) H (R²+r²+Rr)

=(1/3) 4 (6²+1²+61)

=99.304 ft³

Now Density of water = 0.0624 lbm/ft³

Total mass of water in the cone = density volume of cone

= 0.0624 99.304

= 6.196 lbm

Thus time required to fill the cone =

= =0.06196 min

=3.71 seconds

queen_honey_blossom answered 1 year ago

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