## Posts

Showing posts with the label Mechanical Properties of Fluids

### Viscosity, Viscous force and Coefficient of Viscosity

Definition of Viscosity: It is the property of a fluid that opposes the relative motion between its adjacent layers. This property of the fluid is known as viscosity. It is also called the resistance of fluid to flow or deformation or fluid thickness. Effect of temperature on Viscosity: The viscosity of the fluid decreases sharply with the temperature rise and becomes zero at boiling temperature. On the other hand, the viscosity of the gases increases with the temperature rise. Definition of Viscous Force (Internal Frictional Force): When a layer of fluid slide over another layer of the same fluid then an internal tangential frictional force act between them which opposes the relative motion between the layers. This tangential force is called viscous force or internal frictional force. In the absence of external force, the viscous force would soon bring the fluid to rest. Factor affecting the viscous force: There are the following factors that affect the v

### Principle of continuity in fluid

Statement of Principle of Continuity: When an ideal liquid (i.e. incompressible and non-viscous liquid ) flows in streamlined motion through a tube of non-uniform cross-section, then the product of the velocity of flow and area of cross-section is always constant at every point in the tube. Mathematical Analysis (Proof) Let us consider, an ideal liquid (i.e. incompressible and non-viscous liquid ) flow in streamline motion through a tube $XY$ of the non-uniform cross-section. Now Consider: The Area of cross-section $X = A_{1}$ The Area of cross-section $Y = A_{2}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $X = v_{1}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $Y = v_{2}$ The volume of liquid entering at the cross-section $X$ in $1$ second is = $A_{1}v_{1}$ The mass of liquid entering at the cross-section $X$ in $1$ second is = $\rho A_{1}v_{1}$ Similarly, the mass of the liquid com

### Principle, Construction and Working of Venturimeter

Principle of Venturimeter: It is a device that is used for measuring the rate of flow of liquid through pipes. Its principle and working are based on Bernoulli's theorem and equation. Construction: It consists of two identical coaxial tubes $X$ and $Z$ connected by a narrow co-axial tube $Y$. Two vertical tubes $P$ and $Q$ are mounted on tubes $X$ and $Y$ to measure the pressure of the liquid that flows through pipes.. As shown in the figure below. Working and Theory: Connect this venturimeter horizontally to the pipe through which the liquid is flowing and note down the difference of liquid columns in tubes $P$ and $E$. Let the difference is $h$. Let us consider that an incompressible and non-viscous liquid flows in streamlined motion through a tube $X$,$Y$, and $Z$ of the non-uniform cross-section. Now Consider: The Area of cross-section of tube $X$ = $A_{1}$ The Area of cross-section of tube $Y$ = $A_{2}$ The velocity per second (i.e. equal to

### Bernoulli's Theorem and Derivation of Bernoulli's Equation

Statement of Bernoulli's Theorem: When an ideal fluid (i.e incompressible and non-viscous Liquid or Gas) flows in streamlined motion from one place to another, then the total energy per unit volume (i.e Pressure energy + Kinetic Energy + Potential Energy) at each and every of its path is constant. $P+\frac{1}{2}\rho v^{2} + \rho gh= constant$ Derivation of Bernoulli's Theorem Equation: Let us consider that an incompressible and non-viscous liquid is flowing in streamlined motion through a tube $XY$ of the non-uniform cross-section. Now Consider: The Area of cross-section $X$ = $A_{1}$ The Area of cross-section $Y$ = $A_{2}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $X$ = $v_{1}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $Y$ = $v_{2}$ The Pressure of fluid at cross-section $X$ = $P_{1}$ The Pressure of fluid at cross-section $Y$ = $P_{2}$ The height of cross-section $X$ from