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8 m3/s discharge flows through 4 m wide rectangular channel at a velocity of 2 m/s. The hydraulic mean radius of the channel is :?
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8 m3/s discharge flows through 4 m wide rectangular channel at a veloc...
Calculation of Hydraulic Mean Radius of a Rectangular Channel

Given:

  • Discharge = 8 m3/s

  • Width of the channel = 4 m

  • Velocity of flow = 2 m/s



Formula:

  • Hydraulic Mean Radius (R) = (Area of Flow Section) / (Wetted Perimeter)

  • Area of Flow Section = (Width of the Channel) × (Depth of Flow)

  • Wetted Perimeter = (2 × Width of the Channel) + (2 × Depth of Flow)



Solution:

  • Area of Flow Section = 4 m × Depth of Flow

  • Discharge (Q) = Area of Flow Section × Velocity of Flow

  • 8 m3/s = (4 m × Depth of Flow) × 2 m/s

  • Depth of Flow = 1 m

  • Wetted Perimeter = (2 × 4 m) + (2 × 1 m) = 10 m

  • Hydraulic Mean Radius (R) = (4 m × 1 m) / 10 m = 0.4 m



Answer:

  • The hydraulic mean radius of the rectangular channel is 0.4 m.



Explanation:

  • The hydraulic mean radius is a measure of the flow-carrying capacity of a channel or conduit. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter of the channel.

  • In this problem, we are given the discharge, width of the channel, and velocity of flow. Using these values, we can calculate the depth of flow and wetted perimeter of the channel.

  • Once these values are known, we can use the formula for hydraulic mean radius to calculate the value for the rectangular channel.

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8 m3/s discharge flows through 4 m wide rectangular channel at a velocity of 2 m/s. The hydraulic mean radius of the channel is :?
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