The rate of flow in the pipe is approximately 0.0483 m^3/s.
To calculate the rate of flow in this problem, we can use the formula:
Q = A * v
where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the fluid.
First, we need to calculate the cross-sectional area of the pipe. The diameter of the pipe is given as 100 mm, so the radius is half of that, or 50 mm. Converting this to meters gives us a radius of 0.05 m.
The cross-sectional area of the pipe is given by the formula:
A = π * r^2
Substituting the values, we get:
A = 3.1416 * (0.05)^2 = 0.00785 m^2
Now, let's find the velocity of the fluid using the data provided. The head of water on the meter when there is no flow is 3 m (gauge), and the atmospheric pressure head is 10.3 m of water.
The velocity of the fluid can be calculated using the formula:
v = sqrt(2 * g * (h1 - h2))
Substituting the given values, where g is the acceleration due to gravity:
v = sqrt(2 * 9.8 * (3 - 10.3)) = 6.15 m/s
Finally, we can calculate the flow rate by multiplying the cross-sectional area by the velocity:
Q = 0.00785 * 6.15 = 0.0483 m^3/s
Therefore, the rate of flow in the pipe is approximately 0.0483 m^3/s.