Final answer:
The flow rate of water from outlets with different diameters will not be the same due to the principles of fluid dynamics such as the continuity of flow and pressure-velocity relationships outlined by Bernoulli's equation. Pipe diameter, pressure requirements, elevation changes, and flow type (laminar or turbulent) all influence the flow rate.
Step-by-step explanation:
The amount of water (measured in L/min) coming out of each outlet will not necessarily be the same if the inner diameter of each pipe and the outlet are different. The flow rate in pipes is affected by several factors, including the diameter of the pipe. According to the principle of continuity for incompressible fluids, the mass flow rate must be constant along the pipe. Hence the velocity of the fluid must increase as the cross-sectional area (related to diameter) decreases, and vice versa.
For example, let's consider a pipe that tapers to a smaller diameter. According to Bernoulli's equation, as the diameter gets smaller, the velocity of the water will increase, but the pressure will decrease. This is because the conservation of energy must apply for the flowing fluid. So, if a large-diameter pipe and a small-diameter pipe are feeding into a common pipe, the speed and pressure of the fluid from each feed will affect the combined flow.
Moreover, the gauge pressure required to push water through a pipe will also depend on factors such as the elevation of the pipe and the difference in diameter. This is evident in the requirement for a certain gauge pressure to ensure a specific speed of water at the outlet if there is a height difference.
In addition, the flow can be laminar or turbulent, which will affect the flow rate. Laminar flow, characterized by smooth layers of water, is different from turbulent flow, which involves chaotic fluid motion. The type of flow can be predicted by calculating the Reynolds number, which depends on the diameter of the pipe, among other factors.