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Consider the cylindrical tank in Example 4 that has a height of 10 m and a radius of 5 m. Recall that if the tank is full of water, then
10. The work required to empty the tank if it is half full
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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…arrow_forwardA trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x from x = -1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 and the density of water is 1000 kg m³ m s²arrow_forwardNeed step by step solution within 30 minutes.arrow_forward
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