# River Channels: Velocity and Discharge by dargen

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```									River Channels

Geography Department Boston Spa School

Energy Variation
• A still body of water at any point above sea level has a certain amount of stored energy. • This = potential energy available to do work in the river channel. • Its quantity is in proportion the mass of the water body & the height it has to fall. • The kinetic energy of a river is caused by its movement & is derived from potential energy. • Between the two is some loss required to overcome the friction with the bed. • If the channel is steep, the change from potential to kinetic energy is rapid & velocity of the river is high & conversely low gradient, low velocity. • The amount of work done by the river is also affected by the volume of water. The greater the discharge, the larger the total energy. • So large rivers have more energy than small ones.

Velocity & Discharge
• Velocity varies vertically & laterally across the river • Discharge is dependant upon the velocity of water & size of channel at a given point

Q= A x V
e.g. if A = 11.32m2 & V=0.153m/s Q=1.73m3/s • Discharge varies at time of flood & low flow as velocity & cross sectional area varies

Friction of water with the bed
• The effect of the bed is determined by how much of the water comes into contact with it –wetted perimeter & cross sectional area of the channel. • Relationship between the wetted perimeter & the cross sectional area = hydraulic radius R= A/Pw • If the value of the hydraulic radius is high, a large area of water in the cross sectional area is affected by each metre of bed & therefore the frictional effect of the bed is limited. If the value is low, the effect is high (e.g. in a very shallow river) • Friction of the bed of the river itself depends upon how ‘rough’ the bed is – smooth, silty bed has low friction compared to gravel & boulders.

Manning’s Equation
Q= Ax R2/3 x S1/2 N • Formula devised in 1889 • Investigate the total effect of internal friction, bed roughness, channel slope, size & shape & discharge on the velocity of a river.

• If bed roughness increases (n is large), velocity & therefore discharge are reduced. • Useful in estimating the discharge in flood conditions

S = slope, n= Manning’s coefficient of bed roughness, R = hydraulic radius, A = cross sectional area & Q=discharge