Fluid Density
Consider an unknown fluid is continuously flowing through a 1 m diameter pipe at 5 cubic meters per second. If the mass flow rate is 1,000 kg/s, what is the unknown fluid’s density in kg/m^3? Assume constant flow.
Expand Hint
Analyze the final desired units and compare it against the given known units.
Hint 2
For a fluid one dimensional flow:
$$$\dot{m}=\rho Q=\rho Av$$$
where
$$\dot{m}$$
is the mass flowrate,
$$\rho$$
is the density,
$$Q$$
is the volumetric flowrate,
$$A$$
is the cross-sectional flow area, and
$$v$$
is the average flow velocity.
For a fluid one dimensional flow:
$$$\dot{m}=\rho Q=\rho Av$$$
where
$$\dot{m}$$
is the mass flowrate,
$$\rho$$
is the density,
$$Q$$
is the volumetric flowrate,
$$A$$
is the cross-sectional flow area, and
$$v$$
is the average flow velocity.
Since mass flowrate and volumetric flowrate are given, the equation to solve for density is:
$$$\rho=\frac{\dot{m}}{Q}=\frac{1,000kg}{5\frac{m^3}{sec}(sec)}=200\:kg/m^3$$$
$$$200\:kg/m^3$$$
Time Analysis
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