Question

A  canoer  is  aimlessly  paddling  in  the  15  m  wide  rectangular channel  downstream  of  a  dam.    The water depth and discharge in  the channel are 5 m and 175 m3/s respectively.  The dam operator assumes  that  the  channel  is  clear,  and  ‘instantaneously’  ramps  up  the  discharge  to  210  m3/s, creating a surge that moves downstream.  If  the  canoer  is  350  m  downstream  of  the  surge  at  the  instant  that  the  surge  is  created  and  is  able to  paddle  1.5  m/s  more  than  the  speed  of  the  water  below  him,  will  he  make  it  to  the  dock  that is 175 m downstream of him before being hit by the surge? 

Answer 1

of Swage moving downstream and The case is represented is of positive as - here V, and V are velocaties at upstream and downstreain and Vw is velocity of twi Surge . 4. Now, width of chaund= 15m Y = 5m. V,= 175 = 2.333 m/s 5x15 Now, Assume that height of surge is small as compared to depth of flow ie h= Y, -y, is very small as compared toy, c = V-V (velocity of Surge with respect to Burge). Vw = Sgy = 19.81+5 = 7m/s. velocity of cancer with respect to flow = 1.5m/s Canver mw curs ware 7m/s. liguls - - i 350m 175m. y doch time taken by Canser to reach doch t= 175 = 116.675. distance travelled by surge in 116.675 d= 7x 116.678 = 816.67 which is more that (350 +175) that means Surge hits the cancer before he can make it to dock.