Determine the mass flow rate of water through a pipe with a diameter of 3.3 cm when speed at which water travels through the pipe is 2.5 m/s.
in one second, the volume swept out by the water is area*2.5 m (figure area either in liters, cm^3, or m^3, I recommend in cm^3)
volume/sec=(3.3cm/2)^2*Pi*250cm/sec
then mass/sec= volume/sec*densitywater
use density = 1g/cm^3
To determine the mass flow rate of water through a pipe, we can use the formula:
Mass Flow Rate (m_dot) = Density (ρ) × Velocity (V) × Area (A)
First, we need to find the area of the pipe. The formula for the area of a circle (πr^2) can be used, where r is the radius of the pipe.
Given:
Diameter (d) = 3.3 cm = 0.033 m (1 cm = 0.01 m)
Radius (r) = d/2
= 0.033 m / 2
= 0.0165 m
Area (A) = πr^2
= π(0.0165 m)^2
Next, we need to find the density of water. The density of water is approximately 1000 kg/m^3.
Given:
Density (ρ) = 1000 kg/m^3
Now, we can calculate the mass flow rate:
Mass Flow Rate (m_dot) = Density (ρ) × Velocity (V) × Area (A)
= 1000 kg/m^3 × 2.5 m/s × π(0.0165 m)^2
Simplifying this equation will give us the mass flow rate of water through the pipe.
To determine the mass flow rate of water through a pipe, you need to know the density of water, the velocity of water, and the cross-sectional area of the pipe.
1. Density of water: The density of water at room temperature is approximately 1000 kg/m³, but it can vary depending on the temperature and pressure.
2. Velocity of water: You are given that the speed at which water travels through the pipe is 2.5 m/s.
3. Cross-sectional area of the pipe: The cross-sectional area of a pipe can be calculated using the formula for the area of a circle: A = π * r², where r is the radius of the pipe.
To find the radius, divide the diameter by 2:
r = 3.3 cm / 2 = 1.65 cm = 0.0165 m
Now, we can calculate the cross-sectional area:
A = π * (0.0165 m)² = 0.000853 m²
Finally, calculate the mass flow rate using the formula:
Mass flow rate = density * velocity * cross-sectional area
Mass flow rate = 1000 kg/m³ * 2.5 m/s * 0.000853 m²
Mass flow rate ≈ 2.133 kg/s
Therefore, the mass flow rate of water through the pipe is approximately 2.133 kg/s.