Freeboard Method of Estimating Liquid Flow From an Open Pipe

Factors

• Lots of things can affect the volume of flow in a pipe -- some significant factors, and some minor factors that may not even be used in estimates. Major factors include the size and shape of the pipe, the inside surface of the pipe (whether it's smooth or rough), and the slope of the pipe. Pressurizing is a greater factor in closed pipes, but in open pipes pressure is limited to the weight of the water in the pipe. Pipe joints and any other factors that may speed or slow flow can be used but are usually considered to have only a minor effect and may not add a lot more accuracy to your estimate.

Maximum Flow

• With any estimate, you have to start with one or more known values. A good place to start with estimating pipe flow is the maximum possible flow. The maximum flow is a function of the volume of the pipe, the slope, which affects the flow-rate, and the surface, which can create friction. Start by calculating the volume. There are complex formulas to calculate this. Another way is to calculate the volume, then test the flow rate.

Volume

• Calculating volume is the same as calculating the volume for a cylinder then dividing it by half, since an open pipe is half-round. The calculation is height times pi times radius squared, then divide by half. Now you can calculate the maximum volume. Test the flow by dropping something very light in the open pipe and timing how long it takes to travel one foot. Now you know the approximate volume and speed of the pipe at maximum flow -- with no freeboard. For example, if the volume of one linear foot of your open pipe is one gallon, and the pipe flows at a rate of one foot per second (at something less than maximum capacity), you can estimate the maximum flow to be one gallon per second.

Cross Section

• If you were estimating the volume of water flowing through a square channel, every additional inch of depth would have the same volume. In a round pipe, each additional inch of depth has incrementally more volume because its dimension gets wider as it nears the widest point of the pipe -- the center in a round pipe or the top in a half-round pipe. If you know the volume of flow at half the pipe's freeboard, you can extrapolate the flow at every increment of freeboard. To do this, estimate the volume by imagining the cross section of the water in the partially full pipe is a triangle, not a downward facing D-shape. Turn the D into a V and connect to top. Now multiply the width of the top chord (the width of the water) times the depth of the water, times 12 inches as you did to measure the volume of the cylinder. This will give you the volume of a rectangle which, if you divide in half, will give you the volume of an extruded triangle the width and height of your partially filled tube. Now, calculated the volume per second using the speed from your flow test. For greater accuracy, increase this volume by a factor of 10 percent since a V holds less volume than a D. With this value, from any give point of freeboard, in addition to the flow at zero freeboard and full freeboard (which is zero), you can extrapolate an estimate of flow per inch of freeboard.