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I have water in a stainless steel pipe (ID = 0.0381m, OD = 0.0411m) network of roughly 10m length, at 120 bar, roughly 50°C (+ or - 5).

This water is having 7kW of heat transferred into it by a cylinder and piston and

**I am going to assume that ALL of this heat is transferred directly into the water**.

I need to work out whether it is practical for me to use a passive (or active ie with a fan) radiator type design to disperse this heat input into the air, or if I have to use a tank of cool water (assumed to be 20°C), to keep it within it's operating temperatures (90°C is the cut off maximum temperature) and if so, what are the sizes required?

Currently I am thinking about using a tank of cool water and passing the piping through this to cool it, but I need to know the required length of pipe in contact with the body of water to keep the temperature stable.

My mass flow rate (q) varies like a sine wave between 0 and 687.1 litres/minute (at 2hz) and I have been told to take an RMS value of this.

## Homework Equations

q RMS = √(x^2 + ∂^2)

Re=(μ.u.Dh)/μ

## The Attempt at a Solution

My RMS value was determined by my assumption that x = the average value ie the max/2

∴ x=343.55

∂= the standard deviation (?) which I was unsure about and assumed to be the same ie

∂=343.55

∴ RMS of flow rate = 485.9 Litres per minute =

**8.0972 x 10^-3 metres^3 per second**

Re=(ρ.u.Dh)/μ

where

ρ=998.2 (water at 20°C)

μ=1x10^-3 kg/ms

u=1.274.q/d^2=7.106500505 m/s

Dh=4.a.p= 0.00054585171 m

and

d= 0.0381 m

a= [itex]\pi[/itex] .(d/2)^2 = 0.00114009183 m^2

p= [itex]\pi[/itex] .d m

q= 0.008097227 m^3/second

∴ Re= 3832 = transient flow

this is incorrect as I know the flow to turbulent. Is this because I am using an incorrect RMS value?

How do I continue this solution to find my required pipe area or length?

Let me know if more information is required for the solution,

Any help will be massively appreciated!

Thanks,

Chris