Open Channel Flow is flow in which the water surface is at atmospheric pressure. This type of flow occurs in streams, rivers, and even in subsurface drainage pipes. These pipes rarely flow full for any extended period of time.
The main equation used in describing open channel flow is the Bernoulli Equation. This equation can be derived by integrating the expression resulting from the application of Newton's second law to open channel flow. It is an expression of the energy at a flow cross section. The total energy of flow is the sum of the kinetic energy (v squared/ 2g) , the potential energy due to the depth of flow (d), and the potential energy due to the height of the channel above some arbitrary datum (z). Energy is expressed as the energy per unit weight, and has the units of length. If there's no energy lost between sections 1 and 2, then H1 = H2.
Based on the law of energy conservation, the Bernoulli Equation can be used to estimate friction losses in channels or to determine flow rates:. By continuity the volumetric flow rate upstream is the same as the volumetric flow rate downstream, and the energy upstream is the same as the energy downstream, if there is no friction losses. These two equations can be solved simultaneously to determine the flow rate under the gate.
In real flow situations, the velocity is not constant across an entire flow section, due to variations in viscous drag at different distances from the boundary. The true mean velocity head across the section, (v-squared over 2g mean) is not necessarily equal to v-mean squared over 2g. A coefficient can be introduced to express the true velocity head in terms of the mean velocity. This coefficient is called the Coriolis coefficient and the value rarely exceeds 1.15 in constructed channels. However in natural channels that can be subdivided into distinct regions, each with a different mean velocity, the coefficient can be as high as 2. The coefficient is particularly important in times of floods when flow is occurring in the flood plains of a channel. Flow tends to be shallow over the flood plains due to increased roughness.
Hydraulic Jump Video link: https://www.youtube.com/watch?v=GVMkktBeqms
Specify energy, E, is defined as the energy when the bottom of the channel is used as the datum. In moving from one flow section to another, specific energy is conserved only if the channel is horizontal. The concept of specific energy is useful in understanding flow regimes. The velocity may be expressed as the flow rate ,Q, divided by the cross sectional area of flow. This area is a function of flow depth. Thus depth occurs both in the kinetic energy component of flow, and in the potential energy component of flow. For a given specific energy, the smaller the depth the more dominant is the kinetic energy component as depth is in the denominator. For larger depths the potential energy component dominates. Under certain conditions flow may spontaneously switch from being kinetic energy dominant to potential energy dominant. When this occurs a hydraulic jump forms.
For most specific energy values, flow takes place at two depths. There is a minimum energy value at which flow can take place for a specified discharge in a given channel. At this energy value, flow takes place at only one depth. This flow condition is termed critical flow. For specific energy values less that the critical value, backwaters are formed. At depth d1, the potential energy dominates, and the flow is slow and deep. This condition is known as sub-critical flow. At depth d2, kinetic energy dominates, and flow is fast and shallow. This condition is know as super-critical flow.
The equation for critical flow may be determined by noting that the minimum specific energy at which a given flow can occur is when flow is critical. Thus differentiating the expression for critical flow and setting it to zero yields the unique relationship between flow rate and flow depth at critical flow.
The quantity v2/gD is known as the Froude number. At critical flow the Froude number is 1. At Froude numbers greater than 1, flow is super-critical, and at Froude numbers less than 1, flow is sub-critical. Critical flow is of importance in the measurement of flow in open channels. At critical conditions, one depth measurement is sufficient to determine flow rates.
Flumes and weirs are obstructions placed in a channel to measure flow. In general weirs raise the channel invert, and flumes narrow the channel width. With both these devices, critical flow is created in some part of the device. At critical flow one depth measure is sufficient to determine flow rate. The flume shown above is a Parshall flume installed in the Boneyard Creek behind Engineering Hall.