The hydraulic radius for flow in a rectangular duct of cross-sectional dimension H, W is

ANS:B -

The hydraulic radius RRR for flow in a rectangular duct, which has cross-sectional dimensions of height HHH and width WWW, is calculated as: R=Cross-sectional AreaWetted PerimeterR = \frac{\text{Cross-sectional Area}}{\text{Wetted Perimeter}}R=Wetted PerimeterCross-sectional Area​ For a rectangular duct:

• Cross-sectional Area AAA = H×WH \times WH×W
• Wetted Perimeter PPP = 2H+2W2H + 2W2H+2W

Therefore, the hydraulic radius RRR is given by: R=H×W2H+2WR = \frac{H \times W}{2H + 2W}R=2H+2WH×W​ Simplifying further: R=HW2(H+W)R = \frac{HW}{2(H + W)}R=2(H+W)HW​ So, the hydraulic radius RRR for flow in a rectangular duct with dimensions HHH (height) and WWW (width) is HW2(H+W)\frac{HW}{2(H + W)}2(H+W)HW​.