If the average depth of the bay is 20 feet and the distance to 

 the farthest point in the bay is 4 miles, the time, t, it will take 

 for the tide wave to propagate to that point is 



L& 4(5,280] ^,„ , n 07 1 



t = I = - / .-,7 ^ = 832 seconds or 0.23 hour . 



/gdj, /32.2tzUj 



Since this time is significantly less than 12.4 hours, the assumption 

 that the bay surface remains horizontal is quite satisfactory. 



b. By varying the cross-sectional area of the channel, A^, 

 assuming that the channel width, B, remains constant and varying 

 the channel depth, -d, and recalculating the tidal prism as des- 

 cribed above, the effect of channel area on the bay tidal prism 

 can be evaluated and compared with the appropriate equation from 

 the table (Atlantic coast, two jetties, A^ = 5.77 x 10"^ P^-^^). 

 This is done graphically in Figure 5 which shows a plot of P versus 

 Kq from the hydraulic response calculations and from the stability 

 equation. The common point on the two curves is the solution. It 

 yields a channel cross-sectional area of 19,000 square feet (1,765 

 square meters) or a depth of 31.7 feet (9.66 meters). This shows 

 that the 600- by 12-foot design channel would be unstable with a 

 strong tendency to erode. 



Where the hydraulic response curve lies above the stability 

 curve (as in the example) the tidal prism is too large for the inlet 

 channel area and erosion will likely occur until a stable channel 

 develops. If the hydraulic response curve crosses the stability 

 curve twice, the lower point is an unstable equilibrium point from 

 which the channel can either close or scour to the upper stability 

 point. If the hydraulic response curve is substantially below the 

 stability curve at all points, a stable inlet channel is unlikely 

 to develop and the channel should eventually close. 



The stable inlet cross-sectional area depends on other factors 

 (e.g., wave climate, monthly tidal range variations, surface runoff) 

 besides the spring or diurnal tidal prism. As a result, the tidal 

 prism-inlet area equations given in the table only serve as an indica- 

 tion of the approximate stable cross-sectional area. The analysis 

 performed in the example demonstrates that the design channel is 

 very likely to erode to a greater depth; however, that depth, which 

 will fluctuate with time, can vary substantially from the indicated 

 depth of 31.7 feet. 



*********************************** 



VI. SUMMARY 



This report presents simple methods for calculating the maximum 

 channel velocity, bay tidal range, and bay tidal phase lag for a tidal 

 inlet connecting a single bay to the sea. The hydraulic response calcu- 

 lations can then be used to determine the stable channel cross-sectional 

 area for a given channel length, bay geometry, and sea tidal range. 



19 



