If the side of a square sewer is 1000 mm, the diameter of a hydraulically equivalent circular section, is

ANS:D - 1095 mm.

To find the diameter of a circular sewer that is hydraulically equivalent to a square sewer, we need to match the hydraulic characteristics of the two shapes. The hydraulic diameter is a measure of the effective cross-sectional area of a shape in relation to its wetted perimeter. For a square sewer with a side length of 1000 mm, the hydraulic diameter Dh​ is the same as the side length, which is 1000 mm. Now, for a circular sewer, we need to find the diameter D that provides the same hydraulic diameter. The hydraulic diameter for a circular pipe is calculated using the formula: Dh​=4A/P ​ where:

• Dh​ is the hydraulic diameter,
• A is the cross-sectional area,
• P is the wetted perimeter.

For a square, the area A is the square of the side length, and the wetted perimeter P is four times the side length. So, for the square sewer: A=1000×1000 mm^2=1000000 mm^2 P=4×1000 mm=4000 mm Now, substitute these values into the formula: Dh​=4×1000000 mm^2​ /4000 mm =4000000 mm^2/4000 mm ​=1000 mm So, the hydraulic diameter Dh​ of the square sewer is 1000 mm. Now, for a circular sewer, the area A is πD^2/4​ and the wetted perimeter P is πD, where D is the diameter. Now, for the circular sewer: A=πD2​ / 4 P=πD Now, substitute these into the formula: 1000=4×πD2/4^ ​​ 1000=πD^2/πD ​ 1000=D Therefore, the diameter of the hydraulically equivalent circular section is 1000 mm. The provided answer of 1095 mm doesn't match the calculated value. It seems there may be a mistake in the answer or the problem statement. Based on the calculation, the correct diameter should be 1000 mm.