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Pipe resistances in an isothermal liquid system

**Library:**Simscape / Fluids / Isothermal Liquid / Pipes & Fittings

The Local Resistance (IL) block models pressure loss due to user-defined pipe resistances in an isothermal liquid system. You can specify different loss coefficients for forward and reversed flows through the pipe segment. For pipe bends, you can also choose to use the Isothermal Liquid library blocks Pipe Bend (IL) and Elbow (IL) or, for area changes, the Area Change (IL) block.

The loss factor is parameterized by either a constant relationship based on the pipe pressure or by user-supplied tabular data for loss coefficients based on the Reynolds number.

Segments with loss factors that remain constant over a range of flow velocities are calculated as:

$${k}_{loss}={k}_{loss,BA}+\frac{\left({k}_{loss,AB}-{k}_{loss,BA}\right)}{2}\left[\mathrm{tanh}\left(\frac{3\Delta p}{\Delta {p}_{crit}}\right)+1\right],$$

where:

*k*_{loss,AB}and*k*_{loss,BA}are the**Forward flow loss coefficient (from A to B)**and**Reverse flow loss coefficient (from B to A)**parameters, respectively.*Δp*is the pressure difference*p*_{A}–*p*_{B}.

The critical pressure difference,
*Δp*_{crit}, is the pressure differential
associated with the **Critical Reynolds number**,
*Re*_{crit}, which is the flow regime
transition point between laminar and turbulent flow:

$$\Delta {p}_{crit}=\frac{\overline{\rho}}{2}{k}_{loss,crit}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{D}_{h}}\right)}^{2},$$

where:

*k*_{loss,crit}is the loss factor associated with the critical pressure, and is based on an average of the forward and reverse loss coefficients.*ν*is the fluid kinematic viscosity.$$\overline{\rho}$$ is the average fluid density.

*D*_{h}is the segment hydraulic diameter, which is the equivalent diameter of a pipe with a non-circular cross-section: $${D}_{h}=\sqrt{\frac{4}{\pi {A}_{flow}}}.$$, where*A*_{flow}is the**Flow area**.

The loss coefficient can alternatively be interpolated from user-provided Reynolds number and loss coefficient data. The vector of Reynolds numbers can have both positive and negative values, indicating forward and reverse flow, respectively: $${k}_{loss}=TLU(\mathrm{Re}).$$

Mass is conserved through the valve:

$${\dot{m}}_{A}+{\dot{m}}_{B}=0.$$

The mass flow rate through the valve is calculated as:

$$\dot{m}={A}_{flow}\frac{\sqrt{2\overline{\rho}}}{\sqrt{{k}_{loss}}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where *k*_{loss} is the flow
loss coefficient, which is selected between the **Forward flow loss
coefficient (from A to B)** and **Reverse flow loss coefficient
(from B to A)** based on the block flow direction.

Area Change (IL) | Elbow (IL) | Pipe Bend (IL) | T-Junction (IL)