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We are given:

[itex]\dot{m}[/itex]

_{steam}= 4.38kg/s

T

_{steam}= 378K

the steam is saturated 90%

T

_{c}of cooling water = 293.15K

T

_{h}of cooling water = 296.5K

For the tubes in the bundle:

Inner diameter = 2.16cm

Outer diameter = 2.67cm

Re

_{max}= 10,000

The problem I'm having is in calculating the necessary number of tubes in the bundle to keep the Re low enough

I started by calculating the heat duty for the condensing steam:

h

_{f}= 438 kJ/kg

h

_{fg}= 2245 kJ/kg

h

_{1}= 438 + (0.90 * 2245) = 2458 kJ/kg

h

_{2}= 438 kJ/kg

Δh = 2458 - 438 = 2020 kJ/kg

Q = 4.38 * 2020 kJ/kg ≈ 8850 kJ/s = 8850 kW

Next, I calculated the necessary mass flow of the cooling water:

T

_{c}= 293.15K

T

_{h}= 296.5K

ΔT = (296.5-293.15) = 3.35K

C

_{p}= 4.18 kJ/(kg*K)

8850 kJ/s = m * C

_{p}* ΔT

8850 kJ/s = m * 4.18 kJ/(kg*K) * 3.35K

[itex]\dot{m}[/itex]

_{water}= 632kg/s

After I found [itex]\dot{m}[/itex]

_{water}I tried to calculate the maximum velocity in one tube based on the maximum reynolds number. This is where I think I went wrong. This is what I did.

Re

_{max}= 10,000

L = Inner diameter = 2.16cm = 0.0216m

μ

_{water}= 1.002 * 10

^{-3}kg/m*s

ρ

_{water}= 998kg/m

^{3}

v

_{water}= (Re * μ)/(ρ * L)

v

_{water}= (10,000 * 1.002*10

^{-3}) / ( 998kg/m

^{3}* 0.0216m)

v

_{water}= 0.46m/s

I thought that the velocity seemed pretty low, but I went even further to calculate the necessary number of tubes in the bundle:

[itex]\dot{m}[/itex]

_{water}= 632kg/s

v

_{water}= 0.46m/s

ρ

_{water}= 998kg/m

^{3}

A

_{required}= [itex]\dot{m}[/itex]

_{water}/[ρ

_{water}* v

_{water}]

A

_{required}= 632kg/s / [998kg/m * 0.46m/s]

A

_{required}≈ 1.38m

^{2}= 13,800cm

A

_{one tube}= (pi/4)*(2.16cm)

^{2}= 3.66cm

^{2}

So the required number of tubes N

_{t}would be

N

_{t}= (13,800cm

^{2})/(3.66

^{2}) ≈ 3770

This number that I'm getting is way beyond the number of tubes were are allowed to use, which supposed to be in the hundreds. I feel like my mistake is somewhere in my calculation of the velocity, but I've double and triple checked and can't find my mistake. Help would be greatly appreciated!