In the benzene pipeline scenario, the mass flow rate is approximately which value?

In the benzene pipeline scenario, the mass flow rate is approximately which value?

• A. 0.100 kg/s
• B. 0.151 kg/s
• C. 0.200 kg/s
• D. 0.250 kg/s

Answer: (B)

Mass flow rate is found by multiplying the liquid’s density by the volumetric flow rate in the pipe (m_dot = ρ × Q). For benzene near room temperature, the density is about 880 kg/m^3. The problem ties the flow to the pipe’s size and velocity, so the volumetric rate is Q = A × v. Using the given pipe geometry and flow velocity yields a volumetric flow rate around 1.72×10^-4 m^3/s. Multiplying by the density gives m_dot ≈ 0.151 kg/s, which matches the expected answer. Any other option would imply a different volumetric flow rate for benzene (or a different density), which isn’t consistent with the scenario’s data.

Mass flow rate is found by multiplying the liquid’s density by the volumetric flow rate in the pipe (m_dot = ρ × Q). For benzene near room temperature, the density is about 880 kg/m^3. The problem ties the flow to the pipe’s size and velocity, so the volumetric rate is Q = A × v. Using the given pipe geometry and flow velocity yields a volumetric flow rate around 1.72×10^-4 m^3/s. Multiplying by the density gives m_dot ≈ 0.151 kg/s, which matches the expected answer.

Any other option would imply a different volumetric flow rate for benzene (or a different density), which isn’t consistent with the scenario’s data.