Chapter 5, Problem 5.16P

Interpretation Introduction

Interpretation: The forces $F_x\text{and}{F}_z$ necessary to hold the pipe bend stationary is to be calculated.

Concept introduction:

The pipe bend remains stationary if the forces exerted by the fluid on the bend are balanced. The fluid flows through the bend in $x\text{and}z$ directions. Apply the momentum balance in $x\text{and}z$ directions to calculate the force required to hold the bend stationary.

The momentum balance in $x$ direction is,

  ${\displaystyle \sum F_x}={\displaystyle \underset{c.s}{\iint }\rho v_x\left(\overrightarrow{v}.\overrightarrow{n}\right)}dA$

The momentum balance equation in $z$ direction is,

  ${\displaystyle \sum F_z}={\displaystyle \underset{c.s}{\iint }\rho v_z\left(\overrightarrow{v}.\overrightarrow{n}\right)}dA$