Final answer:
Flow rate in fluid dynamics is directly proportional to cross-sectional area and average velocity, and one calculates it using the equation Q = Av. The conservation of mass requires a constant mass flow rate through varying cross-sectional areas in rivers, affecting both velocity and flow rate during changes like entering a delta region. The gradient of a velocity vs. time graph can help determine flow characteristics.
Step-by-step explanation:
The relationship between flow rate and velocity is a fundamental concept in fluid dynamics. The flow rate (Q) of a fluid is directly proportional to both the cross-sectional area (A) through which the fluid flows and the average velocity (v) of the fluid. To calculate the flow rate, you use the equation Q = Av. This indicates that as the velocity or the area increases, so does the flow rate. Applying this to a river delta, as the river spreads out, the area increases, generally leading to a decrease in velocity due to the conservation of mass, provided the flow rate remains constant.
In the case of a river splitting into multiple smaller rivers or a single larger river, you must account for changes in both cross-sectional area and velocity. When calculating the average speed at which water moves in the delta region, take the size and flow rate of the river before it spreads out and the size once it has spread out into consideration. The conservation of mass principle implies that the mass flow rate at both upstream and downstream points must remain constant, implying that Av1 = Av2, where A1 and v1 are the area and velocity upstream, and A2 and v2 are the area and velocity downstream.
When analyzing the velocity vs. time graph, the gradient represents the velocity. If you calculate the gradient of the stationary object for the velocity vs. time graph, you will find that the velocity is zero during that time interval. This is important when considering the onset of turbulence or laminar flow, as these flow types are dictated by velocity and other factors outlined by the problem given for the oil gusher.