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This document contains calculations to determine the volume and mass of benzene in a cylindrical tank of given length, radius, and height. It first derives equations to calculate the volume based on the height and applies them to examples. It then calculates the volume and mass of benzene in the tank for different heights, plotting the results on a graph showing mass increases as height increases.

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CHANDU
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37 views3 pages

3

This document contains calculations to determine the volume and mass of benzene in a cylindrical tank of given length, radius, and height. It first derives equations to calculate the volume based on the height and applies them to examples. It then calculates the volume and mass of benzene in the tank for different heights, plotting the results on a graph showing mass increases as height increases.

Uploaded by

CHANDU
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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a.

 If h=0
r−0
V = L*[(r2*cos-{ })-({r-0}*{√ r 2−(r−0)2})]
r
= L*[(r2*cos-{1})-({r}*{√ r 2−(r )2})]
= L*[(r2*cos-{1})-({r}*{0})]
= L*[(r2*0)-(0)]
= L*[0]
=0

 If h=r
r−r
V = L*[(r2*cos-{ })-({r-r}*{√ r 2−(r−r )2})]
r
V = L*[(r2*cos-{0})-({0}*{√ r 2−(0)2})]
V = L*[(r2*π/2)-(0)]
π
V = L*[(r2*π/2)] = ∗¿r2*L
2

b. Mass of benzene (kg) in the tank if L = 10 ft, r = 2 ft, and h = 4 in.


L = 10 ft = 304.8 cm (1ft = 30.48 cm)
r = 2 ft = 60.96 cm
h = 4 in = 10.16 cm (1 in = 2.54 cm)
r−h
V = L*[(r2*cos-{ })-({r-h}*{√ r 2−(r−h)2})]
r
Substituting values in above equation;
60.96−10.16
V = 304.8*[(60.962*cos-{ })-({60.96-10.16}*{√ 60.962−(60.96−10.16)2 })]
60.96
50.8
V = 304.8*[(60.962*cos-{ })-({50.8}*{√ 60.962−(50.8)2})]
60.96
50.8
V = 304.8*[(3716.122*cos-{ })-({50.8}*{√ 1135.482})]
60.96
V = 141634.1 cm3
Mass of benzene in the tank = Density * Volume
= 0.879 * 141634.1
= 124496.4 g
= 124.4964 kg (1kg = 1000 g)

c.

Length Radius Height Volume Mass


304.8 60.96 0 0 0
138358.
304.8 60.96 10 3 121.617
380990.
304.8 60.96 20 9 334.891
680264. 597.952
304.8 60.96 30 3 3
893.004
304.8 60.96 40 1015932 4
304.8 60.96 50 1374118 1207.85
304.8 60.96 60 1743527 1532.56
304.8 60.96 70 2113902 1858.12
2175.58
304.8 60.96 80 2475071 7
2475.28
304.8 60.96 90 2816029 9
2745.62
304.8 60.96 100 3123574 2
2970.35
304.8 60.96 110 3379241 3
3117.38
304.8 60.96 120 3546518 9
3127.83
304.8 60.96 121.92 3558400 4
Mass of Benzene Vs Height of drum level
3500

3000

2500
Mass of Benzene (kg)

2000

1500

1000

500

0
0 10 20 30 40 50 60 70 80 90 0 0 0
10 11 12

Height of drum level (cm)

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