Question

A longitudinal profile of a river is shown in the figure below. If the average discharge of the river at reach AB is 200 m³/s and increases to 300 m³/s at reach CD, then the stream power from the reach AB to CD will change by a factor of _______. (Round off to two decimal places)
(Use g = 10 m/s², P_water = 1000 kg/m³)

Answer 1

Correct Answer: 0.75

The stream power ω is given by the formula:
ω = ρgQS
where:

• ρ = density of water = 1000 kg/m³
• g = acceleration due to gravity = 10 m/s²
• Q = discharge
• S = slope of the river

The slope S is calculated as the change in elevation divided by the change in distance.
For reach AB:

• Elevation at A = 400 m
• Elevation at B = 300 m
• Distance AB = 20 km = 20000 m
• Slope S_AB = (400 - 300) / 20000 = 0.005

The stream power at AB ω_AB is:
ω_AB = 1000 × 10 × 200 × 0.005 = 10000 W
For reach CD:

• Elevation at C = 150 m
• Elevation at D = 100 m
• Distance CD = 20 km = 20000 m
• Slope S_CD = (150 - 100) / 20000 = 0.0025

The stream power at CD ω_CD is:
ω_CD = 1000 × 10 × 300 × 0.0025 = 7500 W
The change in stream power from AB to CD is given by the factor:
Change factor = ω_CD / ω_AB = 7500 / 10000 = 0.75