Calculate Volumetric Flowrate

[Smiley World]

Hi everyone,
Can anyone help me to solve this question ? please.

Water at 25 °C is circulated from a large tank, through a filter, and back to the tank as shown in the figure below. The power added to the water by the pump is 271 W. Determine the flow rate through the filter. In your solution, use all possibilities to determine the Darcy friction factor (f). What type of fluid flow problem is it? Use the most suitable relation, and compare the results from each method. What is the most accurate method and why? In your submission, state your assumptions and show all analysis procedures. Comment on your final answer.
2nd Sem.

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[Valkarie]

Solution:This is a turbulent flow problem, characterized by a relatively high Reynolds number. This can be determined by using the equation Re = (ρVd)/μ, where ρ is the density of the fluid, V is the velocity, d is the diameter of the pipe, and μ is the dynamic viscosity. In this case, the density of water at 25°C is 998.2 kg/m3, the diameter of the pipe is 0.05 m, and the dynamic viscosity is 1.002 x 10-3 kg/ms. Plugging in these values yields a Reynolds number of 4.94 x 104. As this value is greater than 4000, we can conclude that the flow is turbulent. To determine the Darcy friction factor (f), we can use several possibilities. First, we can use the Colebrook-White equation:f = (-2 log(ε/3.7D + 2.51/Re*√f))where ε is the absolute roughness of the pipe and D is the diameter of the pipe. For this case, we assume that the absolute roughness is 0.1 mm and the diameter is 0.05 m. Plugging these values into the above equation yields a Darcy friction factor of 0.0208. We can also use the Blasius equation to determine the Darcy friction factor:f = 0.079/(Re^0.25)Plugging in the Reynolds number of 4.94 x 104 yields a Darcy friction factor of 0.0211. Finally, we can use the Churchill equation to determine the Darcy friction factor:f = (0.3164/Re^0.25)*(ln(Re) - 0.8)^2.5Plugging in the Reynolds number of 4.94 x 104 yields a Darcy friction factor of 0.0207. The most accurate method for determining the Darcy friction factor is the Colebrook-White equation, as it takes into account both the absolute roughness of the pipe and the Reynolds number. The other two equations do not take into account the absolute roughness, so they are not as accurate.