A fluid (rho = 1200kg / (m ^ 3)) flows through a horizontal 3.0 mm diameter pipe. When the Reynolds number is 1500, the head loss over a 6 m length of pipe is 2 m of that particular fluid. Determine the mass flow rate in kg/hr of the fluid at this condition.
Question
A fluid (rho = 1200kg / (m ^ 3)) flows through a horizontal 3.0 mm diameter pipe. When the Reynolds number is 1500, the head loss over a 6 m length of pipe is 2 m of that particular fluid. Determine the mass flow rate in kg/hr of the fluid at this condition.
Solution
To solve this problem, we need to use the Darcy-Weisbach equation for head loss in pipe flow, which is given by:
h_f = f * (L/D) * (V^2/2g)
where: h_f = head loss f = friction factor L = length of the pipe D = diameter of the pipe V = velocity of the fluid g = acceleration due to gravity
Given that the Reynolds number (Re) is 1500, we are in the laminar flow regime, where the friction factor f can be calculated as:
f = 64/Re
Substituting Re = 1500 into the above equation, we get:
f = 64/1500 = 0.04267
Now, we can substitute the known values into the Darcy-Weisbach equation:
2 = 0.04267 * (6/0.003) * (V^2/2*9.81)
Solving for V, we get:
V = sqrt((2 * 2 * 9.81) / (0.04267 * (6/0.003))) = 14.57 m/s
The mass flow rate (m_dot) can be calculated as:
m_dot = rho * A * V
where: rho = density of the fluid A = cross-sectional area of the pipe = pi * (D/2)^2
Substituting the known values, we get:
m_dot = 1200 * pi * (0.003/2)^2 * 14.57 = 0.052 kg/s
Converting this to kg/hr, we get:
m_dot = 0.052 * 3600 = 187.2 kg/hr
So, the mass flow rate of the fluid at this condition is 187.2 kg/hr.
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