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A 90 km2 catchment has a 4-h unit hydrograph which can be approximated as a triangle. If the peak ordinate of this unit hydrograph is 10m3/s the time base is
  • a)
    120h    
  • b)
    64 h
  • c)
    50 h    
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 90 km2 catchment has a 4-h unit hydrograph which can be approximated...
Let the time base = B(hours)
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Most Upvoted Answer
A 90 km2 catchment has a 4-h unit hydrograph which can be approximated...
Given:
Catchment area = 90 km²
Peak ordinate of unit hydrograph = 10 m³/s

To find:
Time base of unit hydrograph

Solution:
1. Convert catchment area from km² to m²
90 km² = 90 × 10⁶ m²

2. Find the volume of runoff for the given peak ordinate
Volume of runoff = Peak ordinate × Time base
We know that the unit hydrograph can be approximated as a triangle.
Area of triangle = (1/2) × Base × Height
Base = Time base
Height = Peak ordinate
Area of triangle = Volume of runoff

Area of triangle = (1/2) × Time base × 10
Volume of runoff = Area of triangle = (1/2) × Time base × 10

3. Find the time base of the unit hydrograph
Volume of runoff = Catchment area × Runoff coefficient
We know that the unit hydrograph is for a 4-hour duration.
4-hour volume of runoff = Volume of runoff for the given peak ordinate
4-hour volume of runoff = (1/2) × 4 × 10 = 20 m³
Runoff coefficient = 20 / (90 × 10⁶)
Volume of runoff = Catchment area × Runoff coefficient
(1/2) × Time base × 10 = 90 × 10⁶ × (20 / (90 × 10⁶))
Time base = 50 hours

Therefore, the time base of the unit hydrograph is 50 hours, which is option C.
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Community Answer
A 90 km2 catchment has a 4-h unit hydrograph which can be approximated...
90*10^6*1/100 = 1/2B*60*60*10
B = 900000/18000
B = 50 h
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A 90 km2 catchment has a 4-h unit hydrograph which can be approximated as a triangle. If the peak ordinate of this unit hydrograph is 10m3/s the time base isa)120h b)64 hc)50 h d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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