## Chapter 2

Pressure Distribution in a Fluid

## Integral Forms of the Conservation Equations for Inviscid Flows

### Overview

The second chapter is devoted to the derivation of the integral formulation of the governing equations for inviscid compressible flow.

### Sections

#### 2.2 Approach

The equation derivation approach is described.

#### 2.3 Continuity Equation

*Mass can be neither created nor destroyed*

Conservation of mass is applied on a control volume which leads to the continuity equation on integral formulation.

#### 2.4 Momentum Equation

*The time rate of change of momentum of a body equals the net force exerted on it*

Newtons's second law is applied on a control volume leading to the integral formulation of the momentum equation.

#### 2.6 Energy Equation

*Energy can be neither created nor destroyed; it can only change in form.*

The first law of thermodynamics is applied to a control volume leading to the integral formulation of the energy equation.

Study Guide

The questions below are intended as a "study guide" and may be helpful when reading the text book.

- If you would hold your thumb tightly over the upper end of straw filled with water and held vertically, would the water not pour out - explain why. Is there a limit for how heigh a water pilar can be without pouring out? If so, how heigh can it be?
- Show that the pressure difference in a fluid can be calculated as \(\Delta p=-\rho g\Delta z\) starting from Newton's second law (\(F=ma\)), the fluid density can be assumed to be constant.
- Show that the force balancing gravity in a fluid at rest is caused by the pressure gradient.
- Show that the normal of a constant-pressure surface must be aligned with the gravity vector in a fluid at rest.
- How does the hydrodynamic pressure distribution differ in liquids and gases?
- How can we make use of Pascal's law when analysing manometer tubes?
- Describe the implication of buoyancy for immersed bodies and floating bodies, respectively.
- How is the buoyancy of a body immersed in a fluid calculated? Show how this relation is obtained.

Document Archive | |

MTF053_C02.pdf | Lecture notes chapter 2 |

MTF053_Formulas-Tables-and-Graphs.pdf | A collection of formulas, tables, and graphs |