In figure I, T is the period of the tide For any time t, the discharge 

 of the tide is q, Hence , the total discharge (volume of the tidal prism) 

 by definition is 



T 



V=f2 qdt 



Jo (1) 



As a first assumption that q is a sine function it follows that 



where ^ is the maximum value of the tidal discharge, which may be expected 

 at any -tidal cycle, 



Substituting the value of q from equation 2 in equation 1 



m T 



V*Q m 

 Integrating the expression 



J sin-^-dt (3) 



T 



2. 2ift .. T 

 o *'"— dts ^f u) 



Substituting the result in equation 3 



<rf (5) 



or 



u m - t 



CHECK ON FORMULA BA.SED ON FIRST ASSUMPTION 



In order to ascertain the correctness of the formula as derived , the 

 maximum quantity of water which might be expected to pass through an inlet is 

 computed and compared with actual field data of measured flows through cer- 

 tain inlets o The inlets to be discussed, which included Nantucket Inlet, 

 Nantucket Island, Massachusetts 5 Manasquan Inlet, New Jersey; Beaufort Inlet, 

 North Carolina; and Baker's Hauiover Inlet, Florida; were not chosen because 

 of their adaptability to the formula, but because they were the only inlets 

 for which field data were available a 



Nantucket Inlet, the entrance to Nantucket Harbor, is situated on the 

 western shore of Nantucket Island, which lies off the coast of Massachusetts 

 (figure 4.)„ The harbor is a land locked body of water and has but one en- 

 trance, the inlet under discussion „ The tidal prism of the harbor as derived 

 from gaging data taken on 29 December 1938 is given as 431,730,000 cu. ft„ 

 With this value known, the maximum quantity of water which might be expected 



16 



