Final answer:
The flow rate at any point in a pipe remains constant according to the principle of conservation of mass. To find the speed at which the water leaves the pipe, we need to calculate the cross-sectional area at that point. Using the equation Q = Av, we can solve for the velocity at the point.
Step-by-step explanation:
According to the principle of conservation of mass, the flow rate at any point in a pipe remains constant.
This means that the product of the cross-sectional area of the pipe and the velocity of the fluid remains constant.
In this case, the flow rate at point A and point C must be the same.
Therefore, we can use the equation Q = Av, where Q is the flow rate, A is the cross-sectional area, and v is the velocity, to find the flow rate at point C.
We know that the average velocity in the pipe is 10 m/s, and the cross-sectional area of the pipe at point A is larger than at point C.
This means that the velocity at point C must be higher than the average velocity.
To find the speed at which the water leaves the pipe, we need to calculate the cross-sectional area at point C.
Given that the diameter of the pipe is 3.5 cm, we can find the radius by dividing the diameter by 2.
Using the formula for the area of a circle, A = πr^2, we can calculate the cross-sectional area at point C.
Once we have the cross-sectional area and the flow rate, we can solve for the velocity at point C using the equation Q = Av.