Consider a spherical water tank with radius 3 feet. A circular hole with radius 0.7 inches is cut into the bottom of the tank. Initially, the water level in the tank is 2 feet.Determine A(y), the horizontal cross-sectional area of the tank at height y. Then, use Torricelli's Law to determine the time tempty When the tank is empty. (Use 32 ft/s? asthe gravitational constant.)A(y) =temptyseconds

According to Torricelli's law velocity of the water through bottom of the tank when height of water…

Answered: Consider a spherical water tank with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The density of air changes with height. Under some conditions density p, depends on height z, and temperature T according to the following equation where Po and A are both constants. A meteorological balloon ascends (i.e., starts at z = 1 and gains height) over the course of several hours. Complete parts (a) and (b) below. Az P(z,T) = Po e ..... dz v) and that the temperature changes over time (i.e., that T is given by a function T(t)), derive, using the chain rule, an expression for the rate of change of air density, (a) Assuming that the balloon ascends at a speed v (i.e., dt as measured by the weather balloon. Choose the correct answer below. dp Az dT O A. dt T2 dt dp %3D dt Az dT dp С. dt %3D + T dt dp Az) dT O D. dt T2) dt (b) Assume that v = 1, Po = 1, and A = 1 and that when t= 0, T= 1. Are there any conditions under which the density, as measured by the balloon will not change in time? That is, find a differential equation that T must satisfy, if dp = 0, and solve this…
A shell of mass 4 kg is shot upward with an initial velocity of 200 m/sec. The magnitude of the force on the shell due to air resistance is 20 the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m/s². When will the shell reach its maximum height above the ground? The shell will reach maximum height after 18.16 seconds. (Round to two decimal places as needed.) What is the maximum height? The maximum height is 1747 m. (Round to the nearest whole number as needed.) 3 (...) When will the shell reach its maximum height above

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