Example 18.2. Volume and Mass Flow Rates in a Cylindrical Pipe.
Water flows through a cylindrical pipe of internal diameter \(1.0\text{ cm}\text{.}\) (a) If \(1000\text{ L}\) of water flows per minute, what is the velocity of flow in \(\text{m/s}\text{?}\) (b) What is the mass rate of flow in \(\text{kg/s}\text{?}\)
Data: \(\rho_w = 1000\text{ kg/m}^3\text{.}\)
Answer.
(a) \(212\text{ m/s}\text{,}\) (b) \(16.7\text{ kg/s}\text{.}\)
Solution 1. (a)
(a) Let us work with SI units \(\text{(m, kg, s)}\text{.}\)
\begin{align*}
R \amp = 0.5\times 10^{-2}\text{ m}, \\
A \amp = \pi R^2 = 7.85\times 10^{-5}\text{ m}^2 \\
Q \amp = 1000\dfrac{\text{L}}{\text{min}} = \dfrac{1.0}{60}\text{ m}^3\text{/s}.
\end{align*}
Therefore,
\begin{equation*}
v = \dfrac{Q}{A} = 212\text{ m/s}.
\end{equation*}
Solution 2. (b)
(b) By multiplying \(Q\) by \(\rho\text{,}\) the density, we will get the mass current.
\begin{equation*}
\rho_w Q = 16.7\text{ kg/s}.
\end{equation*}