Water flows through cylinder pip of internal diameter 7cm at 2m per second. If the pipe is always half full, them what is the volume of water (in liters) discharged in 10 minutes?
To find the volume of water discharged in 10 minutes, we need to calculate the flow rate and multiply it by the time duration.
Let's break down the steps to get the answer:
Step 1: Calculate the cross-sectional area of the pipe.
The internal diameter of the pipe is given as 7 cm. We can calculate the radius by dividing the diameter by 2. Therefore, the radius (r) is 7/2 = 3.5 cm or 0.035 m.
The cross-sectional area (A) of a cylinder is given by the formula A = πr^2, where π (pi) is a constant (approximately 3.14159).
So, A = 3.14159 * (0.035)^2 = 0.00385 m^2.
Step 2: Calculate the flow rate.
The flow rate is the volume of water passing through the pipe per unit of time. In this case, it is given as 2 m/s.
The flow rate (Q) can be calculated using the formula Q = A * V, where A is the cross-sectional area of the pipe and V is the velocity of water.
Therefore, Q = 0.00385 m^2 * 2 m/s = 0.0077 m^3/s.
Step 3: Calculate the volume of water discharged in 10 minutes.
We are given the time duration as 10 minutes, but we need to convert it to seconds because the flow rate is given in meters per second.
1 minute = 60 seconds
Therefore, 10 minutes = 10 * 60 = 600 seconds.
Now, multiply the flow rate (Q) by the time duration (t) to get the volume (V):
V = Q * t = 0.0077 m^3/s * 600 s = 4.62 m^3.
Step 4: Convert the volume to liters.
1 m^3 = 1000 liters
Therefore, 4.62 m^3 = 4.62 * 1000 = 4620 liters.
So, the volume of water discharged in 10 minutes is 4620 liters.
the cross-section area of the water is
πd^2/8 = 49π/8
So, the water flowing through is
(49π/8 cm^2)(2m/s)(10min) = 2309 liters