Physics 1 Problem Solutions 148

Physics 1 Problem Solutions 148 - 144 Chapt. 15 Fluids the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
144 Chapt. 15 Fluids the water coming out of the primary. The volume of water V accumulated in the catchment measures time: V 0 V is the volume of water remaining in the primary. a) Show that the di±erential bit of water volume sent to the catchment is dV = A h v h dt , where v h is the water velocity at the hole and dt is a time di±erential. HINT: Actually, this is one of those obviously it’s ... things. b) Using the continuity equation Av = Constant and Bernoulli’s equation P + 1 2 ρv 2 + ρgy = Constant show that A h v h = k r V 0 V , where k = A h A 0 R 2 g 1 ( A h /A 0 ) 2 . c) Solve the di±erential equation dV dt = A h v h = k r V 0 V with the initial condition V = 0 at t = 0: i.e., ²nd V explicitly as a function of time. At what time t max does V reach a maximum? What is V max ? At what time t empty is the primary empty? If one drops the 2nd order term in the V ( t ) solution, what would V be at time t empty ? d) Why is the simple water clock
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/16/2011 for the course PHY 2053 taught by Professor Buchler during the Fall '06 term at University of Florida.

Ask a homework question - tutors are online