records are available, is to use the continuity equation, 

 finite-difference form, equation (2) becomes: 



Written in 



" Ae \ At / ' 



(6) 



where V is the average inlet current velocity at a cross section of 

 area A^ over a water level sampling interval, and At, hj,', and hjy 

 are mean bay water levels at the beginning and end of the sampling 

 interval. Measurements of water level at any point in the bay will be 

 representative of the mean bay level for the Helmholtz mode of oscillation 

 of inlet-bay systems. 



This method for predicting inlet velocities is well suited for Great 

 Lakes inlets because inlet and bay geometries are simple and level re- 

 corders are easy to install in the protected bays. The sampling interval 

 should be one-twentieth of T^' or shorter and the stilling well care- 

 fully designed for best results (see Sec. III). 



(3) A Numerical Model . A relatively simple but extremely useful 

 method of modeling inlet-bay hydraulics is to simulataneously solve the 

 equations of motion and continuity. In this model the inlet channel is 

 divided by a flow net into a grid of subchannels and cross sections. 

 The subscripts i and j describe the location of the cell for sub- 

 channels (IC = number of channels) and grid sections (IS = number of 

 sections). The equation of motion for an inlet (eq. 1) rewritten 

 in finite-difference form, and integrated along the axis yields (Seelig, 

 Harris, Herchenroder, in preparation, 1977): 



d^ 



dt 



+ g(hs - h&) 



IS-1 



-E 



i=l 



IC 



z 



IC 



E 



Atj) j=l 



2 



I w^.,- Q I Hi Q B^i H,i 



2.208 D. 



J^ 



-2-J 



-z-J 



(7) 



where Ag and Aj, are the inlet cross -sectional areas at the sea and 

 bay ends of the inlet, and V^j is a weighting function for distributing 

 flow throughout the inlet. The discharge through a grid cell is equal 

 to the weighting function of the cell, W^j, times the total discharge 

 of the inlet, Q. The Manning's friction factor, nij, is determined 



