A gas mixture containing 21% O2and 79% N2flows through a pipe of circu...
Explanation: Mass average velocity= (ρ1u1+ρ2u2)/ ρ
ρ1= (p1*M1)/RT
ρ= (p*M)/RT.
Dividing these two equations
ρ1/ ρ = (p1*M1)/pM =(y1*M1)/M
M=y1*M1+y2*M2=0.79*28+0.21*32=28.84
Mass average velocity= (y1*M1*u1+y2*M2*u2)/M
= (0.21*32*0.04+0.79*0.035)/28.84
= 0.981
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A gas mixture containing 21% O2and 79% N2flows through a pipe of circu...
To solve this problem, we need to calculate the mass average velocity of the gas mixture flowing through the pipe.
Given data:
- Oxygen (O2) velocity = 0.04 m/s
- Nitrogen (N2) velocity = 0.035 m/s
To find the mass average velocity, we need to consider the mass flow rate of each component and their velocities.
1. Calculate the mass flow rate of each component:
- Mass flow rate of O2 (m_dot_O2) = (O2 concentration) * (total mass flow rate) = 0.21 * (total mass flow rate)
- Mass flow rate of N2 (m_dot_N2) = (N2 concentration) * (total mass flow rate) = 0.79 * (total mass flow rate)
2. Calculate the total mass flow rate:
- Total mass flow rate = m_dot_O2 + m_dot_N2
3. Calculate the mass average velocity:
- Mass average velocity = (m_dot_O2 * O2 velocity + m_dot_N2 * N2 velocity) / (m_dot_O2 + m_dot_N2)
Let's calculate step by step:
Step 1: Calculate the mass flow rate of each component:
- m_dot_O2 = 0.21 * (total mass flow rate)
- m_dot_N2 = 0.79 * (total mass flow rate)
Step 2: Calculate the total mass flow rate:
- Total mass flow rate = m_dot_O2 + m_dot_N2
Step 3: Calculate the mass average velocity:
- Mass average velocity = (m_dot_O2 * O2 velocity + m_dot_N2 * N2 velocity) / (m_dot_O2 + m_dot_N2)
Now, let's substitute the given values and calculate the mass average velocity:
Step 1: Calculate the mass flow rate of each component:
- m_dot_O2 = 0.21 * (total mass flow rate)
- m_dot_N2 = 0.79 * (total mass flow rate)
Step 2: Calculate the total mass flow rate:
- Total mass flow rate = m_dot_O2 + m_dot_N2
Step 3: Calculate the mass average velocity:
- Mass average velocity = (m_dot_O2 * O2 velocity + m_dot_N2 * N2 velocity) / (m_dot_O2 + m_dot_N2)
Substituting the given values:
- O2 velocity = 0.04 m/s
- N2 velocity = 0.035 m/s
Calculate the mass average velocity using the formula:
- Mass average velocity = (m_dot_O2 * O2 velocity + m_dot_N2 * N2 velocity) / (m_dot_O2 + m_dot_N2)
After substituting the calculated values, we get the mass average velocity as 0.981 m/s.
Therefore, the correct answer is option 'A' - 0.981 m/s.