A fluid with a density of 790 kg/m³ flows at a rate of 0.05 kg/s through a pipe of radius 2.5 cm. The flow velocity is A) 2.5 cm/s. B) 3.2 cm/s. C) 25 cm/s. D) 32 cm/s.

Question

Quizplus · Accepted Answer

The flow velocity can be calculated using the formula for volumetric flow rate, $Q = A \cdot v$, where $Q$ is the volumetric flow rate, $A$ is the cross-sectional area of the pipe, and $v$ is the flow velocity. First, convert the mass flow rate to volumetric flow rate using the density ($\rho$), $Q = \frac{\dot{m}}{\rho}$, where $\dot{m}$ is the mass flow rate. Given $\dot{m} = 0.05 \, \text{kg/s}$ and $\rho = 790 \, \text{kg/m}^3$, $Q = \frac{0.05}{790}$. The cross-sectional area of the pipe, $A = \pi r^2$, with $r = 0.025 \, \text{m}$, so $A = \pi (0.025)^2$. Thus, $v = \frac{Q}{A}$. Substituting the values, $v \approx 3.2 \, \text{cm/s}$.

A Fluid with a Density of 790 Kg/m3 Flows at a Rate

A Fluid with a Density of 790 Kg/m³ Flows at a Rate