please see this picture of the question: http://chuantu.biz/t4/17/1463651226x182

Question

please see this picture of the question: http://chuantu.biz/t4/17/1463651226x1822618092.png

A horizontal drum, a cross-section of which is shown below, is being filled with benzene (density = 0.879 g/cm^3) at a constant rate m(kg/min). The drum has a length L and radius r, and the level of benzene in the drum is h. The expression for the volume of benzene in the drum is V = L[r^2 cos^-1 (r - h/r) - (r - h) squareroot r^2 - (r - h)^2] Show that the equation gives reasonable results for h = 0, h = r, and h = 2r. Estimate the mass of benzene (kg) in the tank if L = 10 ft, r = 2 ft, and h = 4 in. Suppose there is a sight glass on the side of the tank that allows observation of the height of liquid in the tank. Use a spreadsheet to prepare a graph that can be posted next to the sight glass so that an operator can estimate the mass that is in the tank without going through calculations like that in Part (b).

Explanation / Answer

a) By using above equation for volume of benezene

V=L{r2cos-1(r-h/r)-[(r-h) (r2-(r-h)2)1/2]}

If h=0, V=0, (because cos-1(1)=0 and (r2-(r-h)2)1/2=0)

If h=r, V=90r2L (because cos-1(0)=90 and (r-h)=0)

If h=2r, V=180r2L (because cos-1(-1)=180 and (r2-(r-h)2)1/2=0)

b) Density = mass/volume

Mass of Benzene=density*volume of benzene in drum

First we have to convert ft in to cm and also in into cm, then L=304.8cm, r=60.96cm and h=10.16cm

Also density of benzene=0.879g/cc=0.000879kg/cc

Then substitute all values in the above volume expression,Volume V= 37480000cc

Therefore, Mass of Benzene in the tank=density*volume=0.000879*37480000=32,944.92Kg

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.