Shallow Water Problems in Ship Hydrodynamics 



0.2 0.4 0.6 0.8 1.0 1.2 



s = SHIP SECTION AREA/CANAL SECTION AREA 



Fig, 1 Critical zones for squat in a canal 



be small relative to the mean depth of water, and we can replace (2,3) 

 by its Taylor series expansion with respect to Z, writing 



(U --^ + .,.)(A(x,0) + A^(x,0)Z+ ... - S(x,0) - ,,.) = UAg.(2.ii) 

 On collecting terms of leading order in (2,11) and setting 



Ao= A(x,0) 

 S(x) = S(x,0) 



W(x) = A^(x,0), 



(2,12) 

 (2.13) 

 (2.14) 



we have 



u 



A + UWZ - US = 0, 



i.e. 



633 



