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Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name
Project: Project Name
Project No.: P001
Client: Client Name

Centrifugal Pump System Calculation

This calculation determines the pump system requirements including Total Dynamic Head (TDH), Net Positive Suction Head Available (NPSHa), and settling velocity analysis for slurry systems. All formulas follow the corrected methodology with explicit gauge/absolute pressure handling.
Parameter Symbol Value Notes
Temperature 20.0
Fluid Density (ρ) 1035.33
Viscosity 1.00
Vapor Pressure (P_vapor) 9.573
Flow Rate (Q) 6.988
Pipe Diameter (D) 35.0
Inlet Pressure (P_inlet) 97.50
Discharge Pressure (P_discharge) 110.00
Total Static Head (H_static) 15.00
Suction Static Head (Z_s) 1.10
Suction Friction Loss (P_f,suction) 12.70
Discharge Friction Loss (P_f,discharge) 176.60
Median Particle Size (d50) 100.0
FL Factor (Durand) 0.710
Solid Specific Gravity (S_s) 3.200
Parameter Symbol Value Notes
Pressure Head (H_pressure) 1.231
Suction Friction Head (H_f,s) 1.250
Discharge Friction Head (H_f,d) 17.388
Total Friction Head (H_friction) 18.638
Total Dynamic Head (TDH) 34.87
Differential Pressure 354.15
NPSH Available 18.48
NPSH Required (Estimated (use manufacturer data for selection)) 2.50
NPSH Margin 15.98
Flow Velocity 2.018
Settling Velocity (Durand) 0.851

Step 1: Pressure to Head Conversions

Convert pressure values to head (meters of liquid column).

Formula: $$ H_{pressure} = \frac{(P_{discharge} - P_{inlet}) \times 1000}{\rho \cdot g} $$
Substitution: $$ H_{pressure} = \frac{(110.00 - 97.50) \times 1000}{1035.33 \times 9.81} = 1.231 \text{ m} $$
Formula: $$ H_{f,s} = \frac{P_{f,suction} \times 1000}{\rho \cdot g} $$
Substitution: $$ H_{f,s} = \frac{12.70 \times 1000}{1035.33 \times 9.81} = 1.250 \text{ m} $$
Formula: $$ H_{f,d} = \frac{P_{f,discharge} \times 1000}{\rho \cdot g} $$
Substitution: $$ H_{f,d} = \frac{176.60 \times 1000}{1035.33 \times 9.81} = 17.388 \text{ m} $$
Formula: $$ H_{friction} = H_{f,s} + H_{f,d} $$
Substitution: $$ H_{friction} = 1.250 + 17.388 = 18.638 \text{ m} $$

Step 2: Total Dynamic Head (TDH)

Total Dynamic Head is the total head the pump must develop.

Formula: $$ H_{TDH} = H_{static} + H_{pressure} + H_{friction} $$
Substitution: $$ H_{TDH} = 15.00 + 1.231 + 18.638 = 34.87 \text{ m} $$
Formula: $$ P_{diff} = \frac{H_{TDH} \times \rho \times g}{1000} $$
Substitution: $$ P_{diff} = \frac{34.87 \times 1035.33 \times 9.81}{1000} = 354.15 \text{ kPa} $$

Step 3: NPSH Available (NPSHa)

Note: Inlet pressure is GAUGE. Converting to absolute: 97.50 + 101.33 = 198.82 kPa

Formula: $$ NPSH_a = \frac{(P_{inlet,abs} - P_{vapor}) \times 1000}{\rho \cdot g} + Z_s - H_{f,s} $$
Substitution: $$ NPSH_a = \frac{(198.82 - 9.573) \times 1000}{1035.33 \times 9.81} + 1.10 - 1.250 = 18.48 \text{ m} $$

NPSH Status: Safe

Formula: $$ NPSH_{margin} = NPSH_a - NPSH_r $$
Substitution: $$ NPSH_{margin} = 18.48 - 2.50 = 15.98 \text{ m} $$

Step 4: Flow Velocity

Calculate the flow velocity in the pipe.

Formula: $$ v = \frac{Q/3600}{\pi (D/2000)^2} $$
Substitution: $$ v = \frac{6.988/3600}{\pi (35.0/2000)^2} = 2.018 \text{ m/s} $$

Step 5: Durand Settling Velocity (Slurry Analysis)

For slurry systems, calculate the settling velocity. Settling Status: No Settling - Good Margin

Formula: $$ V_L = F_L \sqrt{2 g D \cdot \frac{S_s - S_L}{S_L}} $$
Substitution: $$ V_L = 0.710 \sqrt{2 \times 9.81 \times (35.0/1000) \times \frac{3.200 - 1.035}{1.035}} = 0.851 \text{ m/s} $$

Summary

The pump must develop a Total Dynamic Head of 34.87 m (equivalent to 354.15 kPa differential pressure). The NPSH Available is 18.48 m with a margin of 15.98 m above the required 2.50 m. For slurry transport, the flow velocity of 2.018 m/s should be compared to the settling velocity of 0.851 m/s.
Created By
Engineer Name
Date: ..........................
Checked
By: .............................
Date: ..........................
Approved
By: .............................
Date: ..........................
Client Approved
By: .............................
Date: ..........................

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