Answer:
Step-by-step explanation:
To find the discharge carried by the river, we need to use the cross-sectional area of the river and the velocity of the water. The cross-sectional area can be found by integrating the width of the river across the depth.If the side slope of the river is 1:1, that means that for every 1 meter of horizontal distance from the centerline, the depth of the water decreases by 1 meter. Using this information, we can set up the following integral to find the cross-sectional area:A = ∫[0,b] (b - x) dxWhere b is the width of the river at the base, and x is the distance from the centerline.Solving this integral, we find that the cross-sectional area is:A = (b^2)/2Now that we have the cross-sectional area, we can use the equation for discharge:Q = VAWhere Q is the discharge, V is the velocity of the water, and A is the cross-sectional area. If S is equal to 210^-4 for all sections, that means that the slope of the river is 210^-4. The velocity of the water can be found using the equation:V = √(SgD)Where S is the slope of the river, g is the acceleration due to gravity (9.81 m/s^2), and D is the depth of the water.If we plug in the values for S, g, and D, we can find the velocity of the water and then use the equation for discharge to find the total discharge carried by the river.For example, if the width of the river at the base is 10 meters and the depth of the water is 5 meters, the cross-sectional area would be:A = (10^2)/2 = 50 m^2The velocity of the water would be:V = √(2*10^-4 * 9.81 * 5) = 1.99 m/sAnd the discharge would be:Q = VA = 50 m^2 * 1.99 m/s = 99.5 m^3/sThis is the total discharge carried by the river.