Final answer:
The density of a liquid with a mass flow rate of 3,234.6 kg/s, velocity of 3.52 m/s, and a pipe diameter of 135.31 cm is approximately 630.7 kg/m³.
Step-by-step explanation:
The question asks to find the density of a liquid, given the mass flow rate, velocity, and diameter of the pipe through which it flows. To find this, we need to use the formula for mass flow rate: \(\dot{m} = \rho \cdot A \cdot v\), where \(\dot{m}\) is the mass flow rate, \(\rho\) is the density, \(A\) is the cross-sectional area of the pipe, and \(v\) is the velocity of the liquid.
First, we calculate the cross-sectional area \(A\) of the pipe using the diameter \(d\) provided, remembering to convert diameter from centimeters to meters:
- \(A = \frac{\pi}{4} \cdot d^2\)
- \(A = \frac{\pi}{4} \cdot (1.3531m)^2\)
- \(A = \pi \cdot (0.67655m)^2\)
- \(A \approx 1.437m^2\)
With the area and the given mass flow rate (\(\dot{m} = 3234.6kg/s\)) and velocity (\(v = 3.52m/s\)), we can solve for \(\rho\):
- \(3234.6kg/s = \rho \cdot 1.437m^2 \cdot 3.52m/s\)
- \(\rho = \frac{3234.6kg/s}{1.437m^2 \cdot 3.52m/s}\)
- \(\rho \approx 630.7kg/m^3\)
Therefore, the density of the liquid is approximately 630.7 kg/m³.