238 



diagram showing the effect of the discharge upon the tides. Such a 

 diagram for the Delaware River at Trenton, near the head of tide, 

 prepared from selected monthly mean high and low waters and dis- 

 charges during the period 1922 to 1926, is shown in figure 80. 



455. The tidal part of many of the larger streams entering the 

 Atlantic Ocean in the United States, terminates abruptly in the rapids 

 at which these rivers drop into the Coastal Plain, or into the sub- 

 merged valleys in which their tidal courses lie. The upstream tidal 

 reaches usually have the capacity to carry the ordinary river discharge. 

 During periods of low discharge the flow in these reaches becomes 

 almost entirely tidal, and in many cases the tidal range then increases 

 toward the head of tide, instead of gradually decreasing upstream. 



456. Distribution of the currents due to Jresh-water discharge. — As 

 fresh water has a less specific gravity than salt water, the salt water 

 usually underruns the fresh at the turn of the current, so that the ebb 

 continues on the surface while the flood current is running in beneath. 

 Numerous meter measurements m.ade at various depths at the mouth 

 of the Hudson River show that the strengths of the ebb currents 

 generally are relatively less than the strengths of the flood in the 

 deeper part of the channel (Special Publication No. Ill, U. vS. Coast 

 and Geodetic Survey). 



457. Difference in tidal range on the opposite sides of a wide estuary 

 because of the earth's rotation. — Unexpected as it may seem, the rota- 

 tion of the earth produces a measurable difference in the tidal ranges 

 on the opposite sides of a wide estuary. Consideration will show that 

 the earth rotates under the moving water in the channel, as it rotates 

 under a Foucault pendulum. At a place whose latitude is X, the rate 

 of rotation is 360° sin X per (siderial) day or 0.000,072,9 sin X radians 

 per second. In the northern hemisphere the currents, if unrestrained, 

 would rotate clockwise at this rate with respect to the earth. Since 

 the direction of the current in a channel is restrained by the banks, 

 the rotation sets up a slight transverse slope of the water surface. 



Designating the rate of rotation of the earth about its axis, in 

 radians per second as co (omega) and the velocity of the current in 

 the direction of the channel by v, the transverse component of the 

 velocity, due to the earth's rotation, if unrestrained, would be uv sin X. 

 Since the steadily exerted force required to restrain a body from mo- 

 tion at a given velocity is twice that necessary to accelerate it to the 

 velocity, the pressure acting on each unit of mass of the flowing water, 

 to restrain it in the direction of the channel is 2uv sin X, and the trans- 

 verse slope to produce this pressure is 2a)z; sin \/g. The difference in 

 level between the two banks of the channel is then 2covz sin X/g, z 

 being the width of the channel. 



458. Ordinarily the flood current in an estuary is near its strength 

 at high water, and the ebb current near its strength at low water. 



