2007-03-23 16:18:46 · 5 answers · asked by Mike G 1 in Science & Mathematics ➔ Engineering
Volume = Pi x r^2 x h where Pi = 22/7; r=radius of trough, h = height.
So Height (h) = Volume / (Pi x r^2)
Hope this helped.
2007-03-23 16:30:02 · answer #1 · answered by Tiger Tracks 6 · 0⤊ 0⤋
I assume the trough is in the shape of a horizontal cylinder cut along the long axis.
Since the cross section of the trough is a semicircle, we'll get help from Pythagoras on this one.
Let's call the radius of the trough r and the width w. The total volume of the trough is
V = Ïr^2w / 2 (the area of the circle cut in half, times the width).
Since the trough is cylindrical, we don't really have to consider the width until we've figured out the area of the cross section of the water.
The depth of the water, measured at the deepest point, is d. Since the trough is partly full, 0 < d < r.
The width of the water from the centre to the edge is s. Thus the water is 2s wide. Since the trough is partly full, 0 < s < r.
The angle theta is the angle whose sine is (r-d) / r.
The water width is s = r cos (theta), or from Pythagoras s=sqrt(r^2-(r-d)^2)
The area of the cross section of the water is the area of the cross section of the trough, minus the triangle from the edge to the centre, minus the sector of the circle above angle theta:
(Ïr^2)/2 - (r-d) sqrt(r^2-(r-d)^2) - 2(theta/360°)(Ïr^2)
Multiply the result by w, and there's your water volume.
2007-03-23 23:45:17 · answer #2 · answered by poorcocoboiboi 6 · 0⤊ 0⤋
Constructing the formula is not hard, but the result is messy. With a partial amount of water in the trough of known depth, calculate the angle between the vertical and the radii to the edges of the liquid. Calculate the area of the isosceles triangle represented by these radii and the liquid surface, and subtract this from the area of the circular sector of the angle determined above. The result is the area of the cross section of the liquid, which can be multiplied by the length of the tank to get the volume. The problem can also be done by integral calculus; this does not make it any easier.
2007-03-23 23:25:50 · answer #3 · answered by Anonymous · 0⤊ 1⤋
Volume=height * (area of cross-section section of the cylindrical trough)
2007-03-24 02:01:06 · answer #4 · answered by Anonymous · 0⤊ 0⤋
V of a cyliner = (Length) x (pi) x radius squared
2007-03-23 23:31:14 · answer #5 · answered by Anonymous · 0⤊ 0⤋