Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of 100 cm2 is filled to a depth of 100 cm with w ? ater. At ? = 0, a drain in the bottom of the tank with an area of 10 cm2 is opened allowing water to flow out of the tank. The depth of water in the ta ? nk at ti?m?e ?t ? 0 is ?? ) = (10 ? ? 2.2?t)2. ? a. Check that d? (0) = 100, as specified. b. What is an appro?priate domain for ?d? c. At what time is the tank first empty?
Step-by-step solution Step 1 of 6 Step 2 of 6 In order to do that we will put the value 0 instead t in the relation d(t) = (102.2t) 2 Now it is proven that the depth of water is equal to 100 cm in the beginning (t=0). Step 3 of 6 T he tank is opened at t=0. Th e domain of function d (t) represent the time from the moment when the tank is opened (t=0) to the moment when the tank is empty. When the the tank is empty the depth of water is equal to zero. Therefore, if we want to findthe domain of function d (t) we must solve the equation d(t)=0. Let’s rearrange this equation.