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Determining the flow rate for a cooling system

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MODERATOR'S NOTE: HOMEWORK INCORRECTLY POSTED TO CLASSICAL FORUM, SO NO TEMPLATE

I need help with the following question:

Please have a look at the question and my attempt at the solution.

Alternative cooling systems are considered for a large computing centre requiring 1 MW of cooling power.(i) One solution is to provide cooling by a heat exchanger interfaced to a cold waterpipe. The water, initially at 10◦C, is taken from a nearby lake.The water coming out of the heat exchanger has a temperature of 15◦C. Whatis the flow rate (in m3s−1)? The specific heat of water is 4200 J kg−1K−.

My attempt at a solution is as follows but uses a dimensional analysis argument and I am unsure whether this is is an appropriate method for tackling the question.

E = mcΔT

But Power = P = E/t = mcΔT/t

Therefore P/cΔT = m/t = Density *Volume /t

But we know density of water is 1000kg m^-3.

So we deduce that P/cΔT*1000 = V/t which has the correct dimensions.

The value I deduce is 0.0476m^3s-1 and am unsure whether that seems reasonable .
 
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I can't tell whether the 1000 is in the numerator or the denominator. Please use parenthesis.
 

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