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

Positive Displacement Pump Calculation

This calculation determines the total differential pressure required by the pump and analyzes the suction conditions to ensure safe operation without cavitation. The analysis includes acceleration head losses which are critical for reciprocating positive displacement pumps.
Parameter Symbol Value Notes
Fluid Density ρ 998 kg/m³
Vapor Pressure P_vapor 2.34 kPa (abs)
Required Flowrate Q 10.5 m³/h
Total Static Head H_static 25.1 m
Suction Static Head Z_s 0 m Liquid level above pump centreline (+ flooded, − lift)
Suction Vessel Pressure P_inlet 101 kPa (gauge)
Discharge Vessel Pressure P_discharge 500 kPa (gauge)
Suction Friction Loss P_f,suction 15.2 kPa
Discharge Friction Loss P_f,discharge 251 kPa
Suction Pipe Diameter D_pipe 50.8 mm
Suction Line Length L 10.5 m
Pump Speed N 150 RPM
Pump Type Type Triplex C = 0.066 (HI, single-acting)
Pump Action Single-acting Sets C for simplex / duplex
Liquid Compressibility Factor K 1.4 HI: 1.4 deaerated water, 1.5 most liquids, 2.0 hydrocarbons, 2.5 hot oil

Step 1: Suction Pipe Velocity

The velocity in the suction pipe is calculated from the flowrate and pipe diameter.

Formula: $$ v = \frac{Q}{3600 \, \pi \, (D_{pipe}/2000)^2} $$
Substitution: $$ v = \frac{10.50}{3600 \, \pi \, (50.80/2000)^2} $$
Result: $$ v = 1.439 \; \text{m/s} $$

Step 2: Total Differential Pressure

The total differential pressure is the sum of static pressure, vessel pressure differential, and friction losses.

Formula: $$ P_{static} = \frac{H_{static} \, \rho \, g}{1000} $$
Substitution: $$ P_{static} = \frac{25.15 \times 998 \times 9.81}{1000} $$
Result: $$ P_{static} = 246.23 \; \text{kPa} $$

Gauge pressures converted with the local atmospheric pressure 101.325 kPa (101.325 kPa at sea level; lower at altitude).

Formula: $$ P_{abs} = P_{gauge} + P_{atm} $$
Substitution: $$ P_{inlet,abs} = 101.33 + 101.325, \; P_{discharge,abs} = 500.00 + 101.325 $$
Result: $$ P_{inlet,abs} = 202.65 \; \text{kPa}, \; P_{discharge,abs} = 601.33 \; \text{kPa} $$
Formula: $$ P_{\Delta vessel} = P_{discharge} - P_{inlet} $$
Substitution: $$ P_{\Delta vessel} = 601.33 - 202.65 $$
Result: $$ P_{\Delta vessel} = 398.68 \; \text{kPa} $$
Formula: $$ P_{friction} = P_{f,suction} + P_{f,discharge} $$
Substitution: $$ P_{friction} = 15.25 + 250.80 $$
Result: $$ P_{friction} = 266.05 \; \text{kPa} $$
Formula: $$ P_{diff} = P_{static} + P_{\Delta vessel} + P_{friction} $$
Substitution: $$ P_{diff} = 246.23 + 398.68 + 266.05 $$
Result: $$ P_{diff} = 910.95 \; \text{kPa} $$

Step 3: Acceleration Head Loss

For a single-acting Triplex pump the Hydraulic Institute acceleration constant C = 0.066 (ANSI/HI 6.1–6.5); K is the liquid compressibility factor. The acceleration head is the pressure needed to accelerate the suction column with the pulsating flow of a reciprocating pump.

Formula: $$ H_{accel} = \frac{L \, v \, N \, C}{K \, g} $$
Substitution: $$ H_{accel} = \frac{10.50 \times 1.439 \times 150 \times 0.066}{1.40 \times 9.81} $$
Result: $$ H_{accel} = 10.89 \; \text{m} $$
Formula: $$ P_{accel} = \frac{H_{accel} \, \rho \, g}{1000} $$
Substitution: $$ P_{accel} = \frac{10.89 \times 998 \times 9.81}{1000} $$
Result: $$ P_{accel} = 106.63 \; \text{kPa} $$

Step 4: Net Positive Inlet Pressure Available (NPIPA)

Liquid level above the pump centreline (negative for a suction lift).

Formula: $$ P_{Z_s} = \frac{Z_s \, \rho \, g}{1000} $$
Substitution: $$ P_{Z_s} = \frac{0.00 \times 998 \times 9.81}{1000} $$
Result: $$ P_{Z_s} = 0.00 \; \text{kPa} $$

NPIPA is the absolute pressure margin available at the pump suction to prevent cavitation (ANSI/HI 6.1–6.5; GPSA Engineering Data Book Sec. 12). All pressures in this calculation are converted to absolute values.

Formula: $$ NPIPA = P_{inlet,abs} + P_{Z_s} - P_{vapor} - P_{f,suction} - P_{accel} $$
Substitution: $$ NPIPA = 202.65 + (0.00) - 2.34 - 15.25 - 106.63 $$
Result: $$ NPIPA = 78.43 \; \text{kPa} $$

Step 5: NPIP Safety Assessment

Status: Safe. NPIPA margin is 43.43 kPa above requirement. System is safe.

Formula: $$ Margin = NPIPA - NPIPR $$
Substitution: $$ Margin = 78.43 - 35.00 $$
Result: $$ Margin = 43.43 \; \text{kPa} $$
Parameter Symbol Value Notes
Suction Velocity v 1.44 m/s
Static Pressure P_static 246 kPa
Vessel Pressure Differential P_Δvessel 399 kPa
Total Friction P_friction 266 kPa
Total Differential Pressure P_diff 911 kPa Pump duty
Total Dynamic Head TDH 93 m
Acceleration Head H_accel 10.9 m
Acceleration Pressure Loss P_accel 107 kPa
NPIP Available NPIPA 78.4 kPa
NPIP Available (head) NPIPA 8.01 m
NPIP Required NPIPR 35 kPa From manufacturer
NPIP Margin Margin 43.4 kPa
NPIP Status Status Safe
Created By
Engineer Name
Date: ..........................
Checked
By: .............................
Date: ..........................
Approved
By: .............................
Date: ..........................
Client Approved
By: .............................
Date: ..........................

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