231 



primary tides and currents will have a constant amplitude, and will 

 advance up the channel at the rate of -^JgD. 



443. To determine the amplitude of the currents, the value of 

 P= 1.084 OV^'S' and P/^S may be computed from the value of S, 

 derived from equation (301): 



S=A7i=Aa/^JgD (318) 



The value of </> may then be obtained from table IX, chapter V. The 

 amplitude of the current is, from equation (308): 



B= {Ag/^/gD) sin 4>=A-^^ sin (319) 



As shown in paragraph 338, the amplitude of current of a friction - 

 less progressive wave, in a channel of uniform dimensions, is: 



The currents m an ideal estuary are therefore less than those set up 

 by a frictionless progressive wave: 



Example. — The mean tidal range at the entrance to the estuary 

 proper of the Delaware River, at Woodland Beach, is 5.63 feet. The 

 mean depth of the estuary at mean tide between Woodland Beach and 

 Philadelphia, taken from maps of about 1918, was found to be 21.5 

 feet. A reasonable value of the Chezy coefficient, C, is 120. Taking 

 the tides as simple harmonic fluctuations with a speed of the AI2 

 component, the constants for computing the form of the ideal 

 estuary are: 



^4=2.815 feet 



a— 0.0001405 radians per second 

 D^r=2l.5 

 C=120 



These values give: 



*S'=0.00001504 

 logP/5'=5.19235 

 = 37°21 



The scaled width of the Delaware at Woodland Beach is 23,000 

 feet, the logarithm of which is 4.36173. The logarithm of the width 

 of an ideal estuary at a point distant x feet upstream, is then, from 

 equation (317) : 



log 2=4.36173-0.000,0030405^ 



In figure 78, page 232, the outline of this ideal estuary is shown 

 in broken lines on a small-scale map of the Delaware. It will be 

 seen that the general shape of the river conforms (y^iite closely to an 

 ideal estuary. 



