# Estimating the Linear Speed of the Currentsfor the Allegheny, Monongahela and Ohio River at Pittsburgh

The volumetric flows at different points along the river are pretty easy to find. One only needs to consult the flow measured at the various dams, readily available in real time through the US Army Corps of Engineers. If it is 10,000 cu. ft./sec. on at the dam at Natrona upstream on the Allegheny, it will be the same on the Allegheny near the point, allowing for a delay so that fluctuations in flow can cover the distance from Natrona to the Point. It has to be the same since the water has nowhere else to go.

It is not so easy when it comes to estimating the linear speed (ft./sec.). For one volumetric flow rate, the speed can vary according to the width and depth of the river. In extreme cases, it will be much faster in the shallows, as everyone knows, for that is where rapids develop on rivers. Fortunately for sailors, there are no rapids in the rivers around the Point, but the effect should still be expected in much smaller magnitude if the river narrows or becomes shallow.

In addition, the linear speed will vary according to position across the river. It will be less near the shallower shores, when frictional drag from the river bottom and other obstructions will slow down the flow. It will less on the inside bend of a river and greater on the outside. These variations can be as high as 25%.

I have found two methods for converting volumetric flow rates into linear speeds. The first is to determine the cross-sectional area of the river. One then recovers the linear speed merely by dividing the volumetric flow rate by the area.

Linear speed (ft/sec)
= Volumetric flow (ft3/sec) / Cross-sectional area (ft2)

Finding the cross-sectional area is not so easy. A cross-section through the river is not a simple shape. It is not, for example, a rectangle whose area could be determined from just the width of the river and the unique depth. The cross-section is a complicated shape that varies in depth across the river. So one needs a complete set of depth soundings across the river to determine the cross-sectional area.

There seems no easy way to acquire this information, short of spending a lot of time on the rivers with a depth sounder. The best source I could find are the sketches of the rivers around the point to which I've linked in navigation charts. These sketches show a profile of the river bed under each bridge. An estimate of the cross-sectional area at each bridge can then be made from the sketches. While I had no initial assurance that these sektches are accurate, the results pertaining to linear speed fit with other information well enough for me to be relatively confident in them. The areas are:

 River Average over locations at bridges listed Average cross- sectional area (ft.2) Allegheny Fort Duquesne, Sixth Street, Seventh Street, Ninth Street, Norfolk and Southern Railroad , Veterans, Sixteenth Street 18,928 Monongahela Fort Pitt, Smithfield, Port Authority Transit, Liberty, Tenth Street, Birmingham 14,500 Ohio West End 31,200

The other method is direct measurement. At a time when you know the volumetric flowrate, time how long it takes debris in the water to cover a distance measured on the shore. The speeds measured for one volumetric flowrate are then scaled linearly to recover the others. This seems unreliable to me largely because I am forced to measure a speed close to shore, where the least representative speeds are to be found. It is also hard to do if there is any wind. Floating debris will be affected by the wind. Debris that sinks, such as a waterlogged piece of driftwood thrown in, will sink away from the wind, but will thereby become impossible to see.

Here is the best data I have. It is only a rough and ready guide. However it gives enough information to enable planning. While these data may be inaccurate, they do suggests that flow rates of 10,000 cu. ft./sec. or less are associated with linear speeds well under 1 mph, which is a range quite hospitable for sailing.

 Flow on the Allegheny River (Cubic feet per second) Speed via cross- sectional area (Miles per hour) Measured and rescaled speed on the Southern shore of the Allegheny river between 7th and 9th Street (Miles per hour) 5,000 .18 .15 10,000 .36 .3 15,000 .54 .45 20,000 .72 .60 25,000 0.9 .75

 Flow on the Monongahela River (Cubic feet per second) Speed via cross sectional area (Miles per hour) 5,000 .235 10,000 .47 15,000 .705 20,000 .94 25,000 1.175

 Flow on the Ohio River (Cubic feet per second) Speed via cross- sectional area (Miles per hour) Measured and rescaled speed on the Northern shore of the Ohio River at the Newport Marina (Miles per hour) 5,000 .11 .05 - .1 10,000 .22 .1 - .2 15,000 .33 .15 - .3 20,000 .44 .2 - .3 25,000 .55 .25 - .5

The measured speeds are given as a range, reflecting contradictory data collected on different days, so these figures are not very accurate

The speed computed via cross-sectional areas is an average of the speeds throughout one cross-section. It is 20% or more larger than the speed measured close to shore in the two cases of the Allegheny and Ohio. This conforms with the expectation of slower speeds near the shore.

To convert linear speeds in miles per hour to feet per second:
1 ft/sec = 0.6818 mph