Flowify | Process Flowsheet Design Tool

1

Slurry Properties

The foundation of the calculation lies in determining the density and concentration of the solid-liquid mixture. The calculator accepts solids mass flow and either liquid flow rate or solids concentration by weight ( $C_w$ ).

Specific Gravity ( $SG_m$ )

SG_m = \frac{100}{\frac{C_w}{SG_s} + \frac{100 - C_w}{SG_l}}

Volume Concentration ( $C_v$ )

C_v = C_w \times \frac{SG_m}{SG_s}

Mixture Flow Rate: $Q_m = \frac{M_{total}}{SG_m \times \rho_{water}}$ . This volumetric flow rate is constant throughout the system and is used for velocity calculations.

2

Critical Settling Velocity

To prevent pipe blockage, the slurry velocity must exceed the critical settling velocity ( $V_L$ ). We employ the Durand correlation using the Schiller & Herbich (1991) form of the Durand factor.

V_L = F_L \times \sqrt{\frac{2 \cdot g \cdot D \cdot \left(\rho_s - \rho_l\right)}{\rho_l}}

Durand Factor ( $F_L$ )

The Durand Factor is normally determined using Durand-Condolios charts however, for simplicity, we use the following approximation.

Schiller & Herbich (1991), Handbook of Dredging Engineering.

F_L = 1.3 \cdot C_v^{0.125}\left(1 - e^{-6.9 \; d_{50,mm}}\right)

3

Friction & Pipe Features

Friction losses are calculated using the Darcy-Weisbach equation, solving for the friction factor $f$ iteratively using Colebrook-White.

Head Loss

h_f = \left( f \frac{L + L_{eq}}{D} + \sum K \right) \frac{V^2}{2g}

FRICTION FACTOR (f)

\frac{1}{\sqrt{f}} = -2 \log \left( \frac{\varepsilon}{3.7 D} + \frac{2.51}{Re \sqrt{f}} \right)

Handling Fittings & Valves

The calculator accounts for local losses using two methods:
• K-Value Method: Direct loss coefficient.
• Equivalent Length (L/D) Method: Adds virtual pipe length.

Feature	Type	Value Used
Entrance / Exit	K-Value	0.5 / 1.0
90° Bend (Long Radius)	L/D	12
90° Bend (Standard)	L/D	18
Reducer	K-Value	0.3
Gate Valve	L/D	13
Check Valve	L/D	135

4

Pump Derating (HR & ER)

Centrifugal pumps experience performance drops when pumping slurry due to solids slip and friction. Two derating factors are used:

Head Ratio (HR) – reduction in head developed by the pump
Efficiency Ratio (ER) – reduction in pump efficiency

While complex methods like Wilson-Addie-Clift exist, we use a simplified 1 - C_v approach for this learning tool, where $ER \approx HR$ .

Total Dynamic Head (TDH)

First, calculate the system head required for the slurry, including static lift, friction losses, and pressure differentials:

TDH_{slurry} = H_{static} + H_{friction} + \Delta H_{pressure}

Head Ratio (HR)

Simplified derating: assumes head reduction tracks solids volume fraction directly. In standard practice, HR is determined from nomographs based on $d_{50}$ and solids SG.

HR = 1 - C_v

Efficiency Ratio (ER)

Pump efficiency also decreases when pumping slurry. For this simplified tool, we assume $ER \approx HR$ .

ER \approx HR = 1 - C_v

Water Equivalent Head

The equivalent "clean water" head required to select a pump from manufacturer curves.

H_{water} = \frac{TDH_{slurry}}{HR}

Water Equivalent Power

The power calculation accounts for both head and efficiency derating.

P_{water} = \frac{Q \cdot H_{water} \cdot \rho_w \cdot g}{3600 \cdot ER}