My Math Forum Write a differential equation for V at time t

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 January 26th, 2010, 07:41 PM #1 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 Write a differential equation for V at time t According to Torricelli's law the time rate of change of the volume V of a water draining tank is proportional to the square root of the water's depth. A cylindrical tank of radius $10 \sqrt[]{\pi}$ centimeters and height 16 centimeters, which was full initially, took 40 seconds to drain. (a) Write a differential equation for V at time t and the two corresponding conditions. (b) Solve the differential equation. (c) Find the volume of water after 10 seconds.
 January 27th, 2010, 02:25 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,130 Thanks: 2339 If the water depth at time t is h, dV/dt = k?h, where k is a negative constant and 0 seconds ? t ? 40 seconds. V = (100?²cm²)h. When t = 0 seconds, h = 16cm, so V = 1600?²cm³; when t = 40 seconds, h = 0cm, so V = 0cm³. ?V= (10?cm)?h, so (10?cm)(dV/dt)/?V = k. Have a go at integrating that (it's convenient to use integration limits of 40 seconds and t) and finishing the question, posting your work so that we can check it. When evaluating k, take care to give it the right units.

 Tags differential, equation, time, write

### torricelli's law for tank draining

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post MathNewb42 Applied Math 0 March 12th, 2013 07:53 AM vivalajuicy Linear Algebra 3 November 13th, 2012 07:33 AM Jan Differential Equations 1 January 5th, 2011 12:54 PM phythagoras1 Applied Math 2 December 24th, 2010 01:54 AM minhson1989 Algebra 1 September 1st, 2007 06:15 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top