A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r / 1 + π 2 above the surface of the liquid.
A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r / 1 + π 2 above the surface of the liquid.
Solution Summary: The author explains that the center of the disk should be positioned at a height of rsqrt1+pi
A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height
r
/
1
+
π
2
above the surface of the liquid.
A water reservoir has the shape of a right circular cone with its circular base of radius R = 160 m at ground
level (z = 0 m). Rain fills the reservoir over the winter; when full, the reservoir depth is h =
summer, water from the reservoir is pumped up to ground level for drinking, irrigation, etc. At the end of the
summer, the volume of water left in the reservoir is only 3/7 of its full capacity.
%3D
70 m. In
(a) Find the depth of the water in the reservoir at the end of the summer.
Answer: Depth = 52.776
m
(b) Find the total work done to lift water out of the reservoir during the summer.
Answer: W = 54461207640
J.
(Recall the density of fresh water: p =
1000 kg/m.)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY