Hydrology EESC BC 3025

Flow in open channels

we need to know some background regarding flow in channels, because of the following questions:

How are water depth and discharge in a stream related?
How does the velocity in a stream change as the amount of water carried by the stream increases?

streams are different from pipes because they do not have a lid!
streamline: a path defined by the motion of fluid elements in a flow; at any point along a streamline, the flow direction is tangent to the streamline. Conceptually, water may not cross streamlines. The density of streamlines is proportional to the flow velocity.

Specific Energy

Bernoulli equation is a good starting point, although it is dealing with a frictionless fluid; over short distances no friction can be assumed
recall the Bernoulli equation, for a frictionless fluid, we can simplify it by: U²/(2*g) + h +z_b = H, U being the average flow velocity (Fig4.2)
the first two terms are the specific energy: U²/(2*g) + h = E, the dimension of E is [L]!
for a certain discharge rate of the stream, we can plot depth of the stream versus its specific energy: there are two depths possible for each value of specific energy! (Fig4.3)

as shown in the previous examples, we can control the criticality of flow by using obstructions
when installing a weir, we will move from subcritical through critcal to supercritical flow (spillway) (Fig4.7)
we would take advantage of this and derive the equation for discharge as a function of the depth of the water above the weir
the following equation describe this relationship for two geometries of weirs:

in many cases, friction does play a big role in stream flow, so we are actually loosing head in the flow (Roughness of a stream)
flow in a channel is described by Manning's equation (Fig4.8):

R_H=wh/(2h+w): Hydraulic radius
k=1 m^1/3s^-1
S: slope
n: roughness coefficient

velocity distribution as a function of depth (Fig4.10), most flow is turbulent, average flow velocity is at a depth of 0.6*total depth

weirs can be used to measure discharge rates as we did in the lab
we can look impirically at the discharrge rate vs. height relationship for a stream without a well-defined weir and can can use this to estimate the discharge rate (Fig4.13, for this particular creek the exponent in the empirical relationship between Q and h is 2.85).
schematic diagram of a stream gaging station (Fig5.2)
velocity distribution as a function of depth (Fig4.10), most flow is turbulent, average flow velocity is at a depth of 0.6*total depth
we can measure the discharge rate by taking measurements at 0.6* depth (from surface) wading through the river (Fig4.11)
Q = U*A = S w_i*h_i*U_i
Small stream gaging
Gaging larger streams and rivers
stream gaging on the Colorado River at Lee's Ferry