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COOLING TOWER WATER BALANCE

Core Principle

A cooling tower operates on a closed-loop recirculation but experiences continuous water loss. The Water Balance accounts for all water entering and leaving the system to maintain a steady-state operation and control dissolved solids concentration.

1. COMPONENTS OF THE WATER BALANCE

INFLOWS (Make-up Water – M)

Water added to replace all losses.

OUTFLOWS (Losses)

1. Evaporation (E): Water lost as vapor to the atmosphere. Largest loss.
2. Drift (D): Liquid water droplets entrained in exhaust air.
3. Blowdown / Bleed-off (B): Intentional purge of concentrated water to control scaling.
4. Leakage & Other Losses (L): Usually small, sometimes grouped with blowdown.

2. THE FUNDAMENTAL BALANCE EQUATION

At Steady State:

Make-up (M) = Total Losses

M=E+D+B+LM=E+D+B+L​

For practical purposes, leakage (L) is often negligible or included in blowdown:

M=E+D+BM=E+D+B

3. DETAILED CALCULATION OF EACH COMPONENT

. Evaporation Loss (E)

• Primary Driver of Cooling. Approximately 1,000 BTU of heat is rejected for every 1 lb of water evaporated.
• Formula 1 (Using Heat Load):

E(gpm)=Q(BTU/hr)1,000×8.34×60E(gpm)=1,000×8.34×60Q(BTU/hr)​

Where QQ = Total heat rejected in BTU/hr.

• Formula 2 (Using Flow & Range – Most Common):

E(gpm)=R(gpm)×ΔT(°F)×0.001E(gpm)=R(gpm)×ΔT(°F)×0.001​

Simplified Rule of Thumb:

E≈R×ΔT1,000E≈1,000R×ΔT​

Where:
R = Recirculation Rate (gpm)
ΔT = Temperature Range (°F) [HWT – CWT]

In Metric:

E(m3/h)=0.00153×R(m3/h)×ΔT(°C)E(m3/h)=0.00153×R(m3/h)×ΔT(°C)

*(Factor 0.00153 ≈ specific heat / latent heat)*

B. Drift Loss (D)

• A very small fraction of recirculation rate.
• Modern towers: 0.0005% to 0.005% of R.
• Older towers: Up to 0.01-0.2%.
• Formula:

D(gpm)=R(gpm)×Drift Rate (as decimal)D(gpm)=R(gpm)×Drift Rate (as decimal)

Example: For R = 1,000 gpm and 0.001% drift:
D = 1,000 × 0.00001 = 0.01 gpm.

C. Blowdown / Bleed-off (B)

• The controlled variable used to manage water quality.
• Purpose: To limit the Cycle of Concentration (COC) by removing water high in dissolved solids.
• Cycle of Concentration (COC or N):

COC=TDSblowdownTDSmake-up=Concentration in systemConcentration in make-upCOC=TDSmake-up

TDSblowdown​​=Concentration in make-upConcentration in system​

D. Relationship Between Blowdown & COC

From mass balance of dissolved solids:

• Solids entering via make-up = Solids leaving via blowdown & drift.

M×TDSM=B×TDSB+D×TDSDM×TDSM​=B×TDSB​+D×TDSD​

Assuming TDSB≈TDSD≈TDSsystemTDSB​≈TDSD​≈TDSsystem​ and DD is very small:

M×TDSM≈B×TDSsystemM×TDSM​≈B×TDSsystem​COC=TDSsystemTDSM≈MB(if drift is neglected)COC=TDSM​TDSsystem​​≈BM​(if drift is neglected)​

More accurately (including drift):

COC=MB+D=E+B+DB+DCOC=B+DM​=B+DE+B+D​​

Therefore, blowdown can be calculated as:

B=ECOC−1−DB=COC−1E​−D​

(This is the key operational formula)