# Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes

## Abstract

We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity–pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff’s law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity–pressure relation satisfied by other empiric laws.

- Authors:

- University of Zagreb, Department of Mathematics, Faculty of Science (Croatia)

- Publication Date:

- OSTI Identifier:
- 22769385

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; FLUID FLOW; PRESSURE DEPENDENCE; THICKNESS; VISCOSITY

### Citation Formats

```
Marušić-Paloka, Eduard, and Pažanin, Igor.
```*Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0345-5.

```
Marušić-Paloka, Eduard, & Pažanin, Igor.
```*Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes*. United States. doi:10.1007/S40314-016-0345-5.

```
Marušić-Paloka, Eduard, and Pažanin, Igor. Thu .
"Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes". United States. doi:10.1007/S40314-016-0345-5.
```

```
@article{osti_22769385,
```

title = {Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes},

author = {Marušić-Paloka, Eduard and Pažanin, Igor},

abstractNote = {We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity–pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff’s law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity–pressure relation satisfied by other empiric laws.},

doi = {10.1007/S40314-016-0345-5},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}