Final answer:
The mass flow rate split between the upper and lower ends of the deflecting wall can be determined using the principle of continuity by setting up an equation involving the velocities and cross-sectional areas of the two sections. By substituting the given values into the equation, the mass flow rate split can be calculated.
Step-by-step explanation:
The mass flow rate split between the upper and lower ends of the deflecting wall can be determined based on the principle of continuity, which states that the mass of fluid entering a pipe is equal to the mass of fluid leaving the pipe. According to the given information, the oil is flowing at a speed of 1.8 m/s through the larger section of the pipe (A₁) and 5.7 m/s through the smaller section (A₂).
Since the mass flow rate in both sections should be the same, we can set up the equation:
m₁v₁ = m₂v₂
where m₁ and m₂ represent the mass flow rates in the upper and lower parts of the deflecting wall, respectively, and v₁ and v₂ represent the velocities of the oil in the respective sections.
With the given velocities and the assumption of equal density, we can calculate the mass flow rates as:
m₁ = p₁A₁v₁ and m₂ = p₂A₂v₂
where p₁ and p₂ represent the densities in the upper and lower sections of the deflecting wall, and A₁ and A₂ represent the cross-sectional areas of the respective sections.
By substituting these expressions into the initial equation, we can solve for the mass flow rate split between the upper and lower ends of the deflecting wall.