Hydraulic Radius Calculator

The following is the step by step process of calculating the wetted perimeter and hydraulic radius for five different shapes. Go through the details and follow them.

• Observe the shape of the object and make a note of the given details.
• Get the formulas for wetted perimeter, area and hydraulic radius.
• Substitute the values in the equations & perform calculations to get the result.

The hydraulic radius is defined as the ratio of the cross-sectional area of the flow to the wetted perimeter. The different channels are rectangle, pipe with full, pipe with part filled, trapezoid, triangle.

The wetted perimeter of a channel is defined as the area of the channel which is in contact with the fluid that it carries. Flow parameters like hydraulic radius, wetted perimeter plays an important role in designing an effective sewerage system.

Below-mentioned is the formulas to find wetted perimeter and hydraulic radius of different shapes.

• The wetted perimeter of full pipe is P = 2πr
• Hydraulic Radius of full pipe R = A/P = πr²/2πr = r/2
• Pipe (less than half)
• Wetted Perimeter P = r * θ and θ = 2 * arccos [(r - h) / r]
• Area A = r² * (θ - sin(θ)) / 2
• Hydraulic Radius R = A/P = [r² * (θ - sin(θ)) / 2]/[r * θ and θ = 2 * arccos [(r - h) / r]] = [r² * (θ - sin(θ)) / 2] / (r * θ)
• Triangular Channel

• Area A = B * y / 2 = y²z
• Wetted Perimeter P = 2 * y * √(1 + z²)
• Hydraulic Radius R = A/P = yz / [2 * √(1 + z²)]
• Rectangular Channel

• Area A = b * y
• Wetted Perimeter P = b + y + y = b + 2y
• Hydraulic Radius R = A/P = (by)/(b + 2y)
• Trapezoid Channel

• Area A = y * (B + b)/2, B = b + 2zy
• Wetted Perimeter P = b + 2 * y * √(1 + z²)
• Hydraulic Radius R = A/P = (by + y²z)/[b + 2 * y * √(1 + z²)]

Example

Question: Calculate the hydraulic radius of a rectangular channel having the base 15 cm, fluid height 12 cm.

Solution:

Given that

The base of the rectangular channel b = 15 cm

Height of the fluid y = 12 cm

Area of the channel A = b * y

= 15 * 12 = 180 cm²

Wetted Perimeter of the rectangular channel = b + 2y

= 15 + 2(12)

= 15 + 24

= 39 cm

Rectangular channel hydraulic radius R = A/P = by/(b + 2y)

= 180/39

= 4.615 cm

Therefore, the hydraulic radius of the rectangular channel is 4.615 cm.

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1. What is the use of hydraulic radius?

Hydraulic radius is a measure of channel flow efficiency. It is one of the main properties that control the amount of fluid discharge of a channel and its ability to move sediments.

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2. What is the difference between hydraulic radius and hydraulic depth?

Hydraulic radius defined as the ratio of cross-sectional area to the wetted perimeter. And hydraulic depth is defined as the depth which, when multiplied by the topwater surface width and is equal to irregular section area. The hydraulic mean depth formula is A/T and the hydraulic radius formula is A/P.

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3. What is the hydraulic radius of the trapezoidal?

The hydraulic radius of a trapezoid R = [h(b+zh)]/[(b + 2h√(1 + z²)]. Where, b is the bottom width of fluid, h is the depth of fluid and z is the width of the channel slope.

4. How do you find the wetted perimeter?

Wetted perimeter is the total length of the channel walls that are in contact with the fluid.

Wetted Perimeter = Area/Hydraulic_Radius.

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