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General resistance in a thermal liquid branch

**Library:**Simscape / Foundation Library / Thermal Liquid / Elements

The Flow Resistance (TL) block models a general pressure drop in a thermal-liquid network branch. The pressure drop is proportional to the square of the mass flow rate. The constant of proportionality is determined from a nominal operating condition specified in the block dialog box.

Use this block when the only data available for a component is the typical pressure drop and flow rate. This block is useful for representing complex components, where it is difficult to determine theoretical pressure loss from the geometry.

The volume of fluid inside the flow resistance is assumed to be negligible. The mass flow rate in through one port must then exactly equal the mass flow rate out through the other port:

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

where $${\dot{m}}_{\text{A}}$$ and $${\dot{m}}_{\text{B}}$$ are defined as the mass flow rates into the component through
ports **A** and **B**,
respectively.

Energy can enter and leave the flow resistance through the thermal liquid ports only. No heat exchange occurs between the wall and the environment. In addition, no work is done on or by the fluid. The energy flow rate in through one port must then exactly equal the energy flow rate out through the other port:

$${\varphi}_{\text{A}}+{\varphi}_{\text{B}}=0,$$

where *ϕ*_{A} and
*ϕ*_{B} are the energy flow rates into the
flow resistance through ports **A** and **B**.

The pressure drop is assumed proportional to the square of the mass flow rate. The square of the mass flow rate is linearized in a small laminar flow region near zero flow, resulting in

$${p}_{A}-{p}_{B}=K{\dot{m}}_{A}\sqrt{{\dot{m}}_{\text{A}}^{2}+{\dot{m}}_{\text{lam}}^{2}},$$

where:

*p*_{A}and*p*_{B}are pressures at ports**A**and**B**, respectively.$${\dot{m}}_{lam}$$ is the mass flow rate threshold for laminar transition.

*K* is the proportionality constant,

$$K=\frac{\Delta {p}_{nom}}{{\dot{m}}_{nom}^{2}},$$

where *Δp*_{nom} is the **Nominal
pressure drop** parameter value and $$\dot{m}$$_{nom} is the **Nominal mass flow
rate** parameter value.