Question

formula 5 points
water (density = 997.1 kg/m^3 = 62.25 lb_m/ft^3) is flowing through a circular pipe. given that the water flows through a 67 mm diameter pipe with a mass flowrate of 73 kg per minute, what is the velocity of the water in the pipe, expressed as cm/sec? report your answer to two decimal places.

Explanation:

Step1: Convert mass - flow rate to kg/s

The mass - flow rate is given as 73 kg/min. To convert it to kg/s, divide by 60.
$m = \frac{73}{60}\text{ kg/s}\approx1.2167\text{ kg/s}$

Step2: Calculate the cross - sectional area of the pipe

The diameter of the pipe $d = 67\text{ mm}=0.067\text{ m}$. The cross - sectional area of a circular pipe $A=\pi(\frac{d}{2})^2$.
$A=\pi(\frac{0.067}{2})^2=\pi\times(0.0335)^2\approx3.526\times 10^{-3}\text{ m}^2$

Step3: Use the mass - flow rate formula to find velocity

The mass - flow rate formula is $\dot{m}=
ho Av$, where $\dot{m}$ is the mass - flow rate, $
ho$ is the density, $A$ is the cross - sectional area, and $v$ is the velocity.
We know $\dot{m}\approx1.2167\text{ kg/s}$, $
ho = 997.1\text{ kg/m}^3$, and $A\approx3.526\times 10^{-3}\text{ m}^2$.
We can solve for $v$: $v=\frac{\dot{m}}{
ho A}$
$v=\frac{1.2167}{997.1\times3.526\times 10^{-3}}\text{ m/s}$
$v=\frac{1.2167}{3.5157}\text{ m/s}\approx0.346\text{ m/s}$

Step4: Convert velocity to cm/s

Since $1\text{ m}=100\text{ cm}$, then $v = 0.346\times100\text{ cm/s}=34.60\text{ cm/s}$

Answer:

$34.60$ cm/s