Question

Consider a river that spreads out in a delta region on its way to the sea. Calculate the average speed at which water moves in the delta region, based on the speed at which it was moving up the river. Assume the river spreads out into multiple smaller rivers. Given the size and flow rate of the river before it spreads out and its size once it has spread out, find the average speed in the delta.

A) 2.5 m/s
B) 5.0 m/s
C) 7.5 m/s
D) 10.0 m/s

Answer 1

To calculate the average speed at which water moves in the delta region, use the formula v2 = Q1 / A2, where Q1 is the initial flow rate and A2 is the new cross-sectional area. Once you have the ratio of the initial flow rate to the new cross-sectional area, you can find the average speed.

Step-by-step explanation:

To calculate the average speed at which water moves in the delta region, we need to consider the conservation of mass. The volumetric flow rate (Q) of water is equal to the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

Before the river spreads out, the volumetric flow rate will be constant, so we can write the equation as Q1 = A1 * v1, where A1 is the initial cross-sectional area and v1 is the initial velocity.

Once the river spreads out, the cross-sectional area increases while the volumetric flow rate remains constant. Therefore, we get Q2 = A2 * v2, where A2 is the new cross-sectional area and v2 is the new velocity in the delta region. Rearranging this equation gives us the formula v2 = Q1 / A2.

To calculate the average speed, we need to find the ratio of the initial flow rate to the new cross-sectional area. Once we have this ratio, we can substitute it into the equation to find the average speed in the delta region.