the answer is not 14.9 min

Solve for Time to reach steady state

the steady state volume is 228.57L, can you provide the work to solve for the time to reach steady state? Time to Reach Steady-State Write a differential balance on the water in the tank for the period from the moment the input rate is decreased (6-0) to the attaininent of steady statet - - -), expressing it in the formdVid --- Write an intial condition, separate variables, and integrate to fud an expression terve Use the pression to find the time in minutes required for the volume to decrease to within 2.00% of its steady state value min Water is added at varying rates to 3 4000 liter holding tank When a valve in a discharge line is opened, water flows out at a rate proportional to the height and hence to the volume of water in the Lank The flow of water into the tank is slowly increased and the livet rises in consegue until at a steady input rate of 700 /min the level just reaches the top but does not spill over The input rate is then abruptly decreased to 400 min Steady State Volume Weito the eastion that relates the discharge rate (min) to the volume of water in the tank and use it to calocate the tady-state volane when the partis 400/min. Water is added at varying rates to a 400.0-liter holding tank. When a valve in a discharge line is opened, water flows out at a rate proportional to the height and hence to the volume V of water in the tank The flow of water into the tank is slowly increased and the level rises in consequence until at a steady input rate of 70.0L/min the level just reaches the top but does not spill over The input rate is then abruptly decreased to 40.0L/min. Steady-State Volume Write the equation that relates the discharge rate V L/min) to the volume of water in the tank (L), and use it to caludate the steady-state volume when the input rate is 400L/min Time to Reach Steady-State Write a differential balance on the water in the tank for the period from the moment the input rate is decreased (t-0) to the attainment of steady state(t -- ), expressing it in the form dv/dt. Write an intial condition, separate variables, and integrate to find an expression for VCE), Use the expression to find the time in minutes required for the volume to decrease to within 2.00% of its steady-state value. min Water is added at varying rates to a 400.0-liter holding tank. When a valve in a discharge line is opened, water flows out at a rate proportional to the height and hence to the volume V of water in the tank. Lihe flow of water into the tank is slowly increased and the level rises in consequence, until at a steady input rate of 700 L/min the level just reaches the top but does not spill over The input rate is then abruptly decreased to 400 L/min. Steady-State Volume Correct. Write the equation that relates the discharge rate Vout (L/min) to the volume of water in the tank V(L), and use it to caluclate the steady-state volume when the input rate is 40.0 L/min. D 228.57 L double check the bases of the exponential/logarithm functions that you might be using Write a differential balance on the water in the tank for the period from the moment the input rate is decreased (4-0) to the attainrnent of steady state(t - ) expressing it in the form dv/dt-... Write an intial condition, separate variables, and integrate to find an expression for Vio Use the expression to find the time in minutes required for the volume to decrease to within 200% of its steady-state value. min Hint Assistance Used There is one input term and one output term. The solution involves integration