The mass flow rate of n-hexane (density = 0.659 g/cm
) in a pipe is 65.9 g/s. What is the volumetric flow rate of the hexane? A. 0.1 cm
/s B. 0.010 cm
/s C. 100 cm
/s D. 10 cm
/s
The Correct Answer and Explanation is:
The correct answer is C. 100 cm³/s.
Here is a step-by-step explanation of how to arrive at this answer.
The problem requires finding the volumetric flow rate of n-hexane using its given mass flow rate and density. The key to solving this is understanding the relationship between these three physical quantities.
Key Concepts:
- Density (ρ): This is an intrinsic property of a substance, defined as its mass per unit volume. In this problem, the density of n-hexane is 0.659 g/cm³.
- Mass Flow Rate (ṁ): This measures the amount of mass of a substance that passes a specific point per unit of time. The given mass flow rate is 65.9 g/s.
- Volumetric Flow Rate (Q): This measures the volume of a substance that passes a specific point per unit of time. This is the value we need to find, and its units will be cm³/s.
The Relationship:
The fundamental formula connecting mass (m), volume (V), and density (ρ) is:
Density = Mass / Volume (ρ = m/V)
This relationship also applies to flow rates. By dividing both mass and volume by time (t), we get the formula for rates:
Density = (Mass/Time) / (Volume/Time)
Density = Mass Flow Rate / Volumetric Flow Rate
ρ = ṁ / Q
Calculation:
To find the volumetric flow rate (Q), we can rearrange the formula:
Volumetric Flow Rate = Mass Flow Rate / Density
Q = ṁ / ρ
Now, we can substitute the given values into this equation:
- Mass Flow Rate (ṁ) = 65.9 g/s
- Density (ρ) = 0.659 g/cm³
Q = (65.9 g/s) / (0.659 g/cm³)
Q = 100
To determine the final units, we analyze the units from the calculation:
(g/s) ÷ (g/cm³) = (g/s) × (cm³/g)
The grams (g) unit in the numerator and denominator cancels out, leaving cm³/s.
Therefore, the volumetric flow rate is 100 cm³/s, which corresponds to option C.thumb_upthumb_down
