Final answer:
The statement regarding uniform velocity distribution in a wide channel is false due to the velocity varying because of boundary friction, which is explained through fluid mechanics principles. The assumption of zero velocity can be checked with the continuity equation, which evaluates flow rate conservation. The correct option is 2.
Step-by-step explanation:
Is the velocity distribution uniform in a wide channel? The answer is false. In fluid mechanics, the concept that the velocity of fluid varies across a cross-section of a channel or pipe is well established. This is because of the no-slip condition at the boundary where the fluid is in contact with the channel surface; friction slows down the fluid creating a velocity profile that is typically parabolic in laminar flow or flatter with a sharp drop near the walls in turbulent flow. Hence, fluid near the walls moves slower than fluid in the center.
The assumption that the water velocity in the barrel is approximately zero can be checked using the continuity equation, which essentially states that the flow rate must be conserved at all cross-sections of a stream. This can lead us to determine if the velocity at a certain point is realistic given the flow conditions and the cross-sectional area where the water is flowing.
Waves do indeed propagate faster in a less dense medium if the stiffness of the medium remains unchanged. This is a feature of wave mechanics, where the speed of wave propagation is influenced by both the medium's density and its elastic properties.
Regarding the unreasonable results of a stream's flow rate, to calculate the average velocity of the stream, we can use the formula velocity = flow rate/area. With a given width and depth, the area is 10.0 m * 2.00 m = 20.0 m². For a flow rate of 100,000 m³/s, the velocity would be 5,000 m/s, which is an unreasonably high speed for water in a natural stream, indicating either the flow rate or the dimensions provided are inconsistent with reality.
Hence, Option 2 is correct.