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Water from an upper tank is drained into a lower tank through a 5 cm diameter iron pipe with roughness 2 mm. The entrance to the pipe has minor loss coefficient 0.4 and the exit has minor loss coefficient of 1, both referenced to the velocity in the pipe. The water level of the upper tank is 4 m above the level of the lower tank, and the pipe is 5 m long. You will find the drainage volumetric flow rate. a) What is the relative roughness

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Answer:

Relative roughness = 0.04

Explanation:

Given that:

Diameter = 5 cm

roughness = 2 mm

At inlet:

Minor coefficient loss [tex]k_{L1} = 0.4[/tex]

At exit:

Minor coefficient loss [tex]k_{L2} = 1[/tex]

Height h = 4m

Length = 5 m

To find the relative roughness:

Relative roughness is a term that is used to describe the set of irregularities that exist inside commercial pipes that transport fluids. The relative roughness can be evaluated by knowing the diameter of the pipe made with the absolute roughness in question. If we denote the absolute roughness as e and the diameter as D, the relative roughness is expressed as:

[tex]e_r = \dfrac{e}{D}[/tex]

[tex]e_r = \dfrac{0.2 }{5}[/tex]

[tex]\mathbf{e_r = 0.04}[/tex]

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