Question 14Air is flowing in a 0.2 meter diameter pipe at a uniform velocity of 0.5 m/s. The temperature is 49 °C and pressure is 99 kPa. Determine the mass flow rate in kg/s.1 point
Question
Question 14Air is flowing in a 0.2 meter diameter pipe at a uniform velocity of 0.5 m/s. The temperature is 49 °C and pressure is 99 kPa. Determine the mass flow rate in kg/s.1 point
Solution
To solve this problem, we need to use the equation for mass flow rate, which is:
Mass Flow Rate = Density * Velocity * Area
First, we need to find the density of the air at the given temperature and pressure. We can use the ideal gas law for this, which is:
Density = Pressure / (R * Temperature)
Where:
- Pressure (P) is 99 kPa or 99000 Pa,
- R is the specific gas constant for air, which is 287 J/(kg*K),
- Temperature (T) is 49 °C or 322 K (remember to convert from Celsius to Kelvin by adding 273.15).
So, Density = 99000 / (287 * 322) = 1.07 kg/m^3
Next, we need to find the cross-sectional area of the pipe. We can use the formula for the area of a circle, which is:
Area = π * (Diameter/2)^2
So, Area = 3.1416 * (0.2/2)^2 = 0.0314 m^2
Finally, we can find the mass flow rate by multiplying the density, velocity, and area:
Mass Flow Rate = 1.07 kg/m^3 * 0.5 m/s * 0.0314 m^2 = 0.0168 kg/s
So, the mass flow rate of the air in the pipe is approximately 0.0168 kg/s.
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