- Q1 Refer To The Slide Example 5 Below Example 5 Draining A Tank A Right Circular Cylindrical Tank With Radius 5 Ft An 1 (103.82 KiB) Viewed 38 times
Q1 Refer to the slide "Example 5" below: EXAMPLE 5 Draining a Tank A right circular cylindrical tank with radius 5 ft and height 16 ft that was initially full of water is being drained at the rate of 0.5√x ft³/min. Find a formula for the depth and the amount of water in the tank at any time t. How long will it take to empty the tank? Solution The volume of a right circular cylinder with radius r and height his V = πr²h, so the volume of water in the tank (Figure 9.4) is V = πr²h = π(5)²x = 25mx. Diffentiation leads to dV di Thus we have the initial value problem -0.5√x = 25m dx dt x(0) 25T Vx 50T = 16 dx dt dx dt Negative because Vis decreasing and dx/dt < 0 Torricelli's Law The water is 16 ft deep when/= 0.
Q1 (cont.) dx √x Solve the initial value problem -,x(0) = 16. dt 50T Specifically, plot the function of x(t) for a length of 0 ≤t ≤to, where to is the length of time it takes for the tank to become fully empty. Figure out a way to manually estimate the value of to.