Please help physic question !?
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
- Anonymous2 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.