Waste water is pumped from a tank located 40 meters below ground at a flow rate 10m3/hr . Calculate the minimum pump size . Take waste water specific gravity as 1:10

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• Anonymous
2 months ago

By pump size, I guess you mean its power (assuming 100% efficient).

Specific gravity can't be 1:10.  I guess you mean 1.10 so since density of water = 1000kg/m³, the density of the waste water = 1.10*1000 = 1100 kg/m³

Volume per second = 10/3600 m³/s, so mass per second is m = 1100 * 10/3600 = 3.05556 kg/s.

Potential energy gained per second = mgh

= 3.05556 * 9.8 * 40 = 1200 J/s = 1200W

You may think that a 1200W pump is required.  But note each second  3.05556kg is moved a distance 40m.  That's an average speed of 40m/s.  Se everry second, 3.05556kg is accelerated from 0 to  40m/s.  The kinetic energy supplied to the water per second is

½mv²  = ½*3.05556*40² =  2444J/s = 2444W

So the pump must  have a minimum power of 1200+2444 = 3600W rounded to 2 sig. figs.

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