Question

I only want the answer for No 2

Note: The time it takes to get a two-liter bottle empty is given in the picture

I only want the answer for No 2

Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a hole with area a at the bottom of the tank, then Torricelli's Law says that dV dt where g is the acceleration due to gravity. So the rate at which water flows from the tank is proportional to the square root of the water height. 1) Suppose the tank is cylindrical with height 6 feet and radius 2 feet and the hole is circular with radius 1 inch. If we take g 32 , show that h satisfies the differential equation dh 1 dt 72 Pay attention to your units when showing the work for this problem 2) Because of the rotation and viscosity of the liquid, the theoretical model given by our first equation isn't quite right. Instead, the model dV dt is often used and the constant k is determined experimentally. Use the associated video of a draining tank to determine the value of k for water draining from a 4-mm hole in a two-liter bottle. Then, find an expression for h(t) and determine the time it would take for the water level to go from 10 cm all the way down to 0 cm. - - - 00:01:38.910 01:48/01:48

Answer 1

Solu Hon givem dv Let any time t the h(4) hight of the h dpond on hime 2 2 k .dt th) 2. TTr 2.

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