13.1.5. Pressure and Viscosity

Now if you look at the fluid properties what we have some of the fluid properties if you know it is related to the dimensions okay that is the length area and the volume. So it is just a dimension and geometric dimensions so it has only unit in terms of the length okay. So that means length is L1 L2 and area will be L2 the volume will be L3 so you can understand what is the velocity you know it length power unit time. The acceleration similar way you can do it let me look at what is the distance or volumetric rate volume or unit time that is what we Lq divide by That will be the volumetric then now we have come to the 2 different parts one is Kinematic viscosity as we discuss in newtons laws of viscosity is that it is independent of mass. So you can understand it has a dimensions of length and time. Similar way we see a Strain rate also indifferent of mass and length.

Fluid properties such as length, area, and volume are crucial in understanding fluid mechanics. These dimensions help in defining velocity and acceleration. The text explains how dimensions correlate to fluid properties, emphasizing the significance of kinematic viscosity (which is related to shear stress and strain rate) as being independent of mass and defined by length and time. Understanding these dimensions allows for the classification and analysis of different fluid behaviors.

Think of a river where the width (length) and the depth (volume) of the river affect how quickly the water flows. Kinematic viscosity can be likened to how molasses pours slowly compared to water, showcasing how different fluids behave based on their viscosity, independent of their mass.

Now if you look at other part like pressures force per unit area similarly case force per unit area. So force you know it that will be the mass into acceleration the force will be mass into acceleration the pressure and stress will be the force per unit area. That is what you can compute it. Similar way you can compute the viscosity dimensions if you know very basic equation of Newtons law of viscosity. Just Shear stress rate is proportional to Shear strain rate proportionality is the viscosity.

Pressure is defined as force per unit area, which means it's crucial to understand how forces (like weight or thrust) affect fluids. The text discusses how viscosity relates to shear stress and strain rate through Newton's law of viscosity. If a fluid is subjected to a shear force, the rate at which it flows (or its strain) is proportional to the viscosity. This principle is fundamental in determining how fluids behave under pressure or when forces are applied.

Imagine pushing a thick syrup over a surface. The force you need to apply to keep it moving relates directly to the syrup's viscosity. If you push it too hard (high shear stress), the flow will increase at a rate that reflects its viscosity – just like heavy traffic on a busy road, where the 'strain' on the road (vehicles moving) is related to how many cars and how fast they're driven.

Let us go for what is the principal of homogeneity all the equations not all the equations so most of the questions in engineering the most of the equations of engineering dimensionally homogenous not all that is the let me have a repeat these things that means what it indicates as that the dimensions of the equations will be the same okay the left side of dimensions LHS should have a dimensions of right hand side. Then the equations are dimensionally homogeneous so that means what do we have to look at that for any physical political properties is and all so somewhere it follows this dimensional homogeneous concept.

Dimensional homogeneity means that the dimensions of physical quantities in an equation must match. For example, in a fluid dynamics equation, both sides of the equation should represent quantities with the same dimensions, ensuring consistency. This concept is crucial for verifying equations in fluid mechanics, as it helps ensure that all derived equations and relationships accurately describe fluid behavior.

Consider a balance scale; if you place an object of a certain weight on one side, to keep it balanced, the other side must equal that weight. In fluid equations, just like the scale, everything must have 'weights' (dimensions) that match up to maintain balance (truthfulness) in calculations.

So the drag force what is happening is it is a function of D is the diameter of the cylinder V is the velocity of the flow. And the rho and the mu is the fluid properties related to density and the dynamic viscosities the viscous force components it depends upon the like you can know it the drag force court in oil will be the different compared to drag force in air. So that with the mu will take care of what type of drag force will be there D also depends if a bigger diameter or smaller diameter D also matters.

When studying drag force on an object like a cylinder in fluid flow, many variables come into play: the diameter of the cylinder (D), the velocity of the fluid (V), and the properties of the fluid, such as density (ρ) and dynamic viscosity (μ). Every change in these parameters can significantly affect the drag experienced by the object, illustrating the importance of experimental analysis in understanding fluid dynamics.

Think about swimming in water versus biking in air. In water, your body experiences drag based on the density of the water, the speed you swim, and your body's shape (like a larger swimmer causing more drag). This is similar to how the drag force on the cylinder varies with fluid characteristics, emphasizing how changes in one parameter can lead to varied experiences.

So the non dimensionless experiments making us that we can make a dimensionless force plot. And we can conduct the experiment with the different Reynolds numbers and plot because once you do with different Reynolds experiment you will get the course you know the velocity you move the diameters of the cylinders then you can compute it what will be the non dimensionless force component here.

Dimensional analysis allows us to create dimensionless quantities, enabling the establishment of relationships between fluid properties and behaviors without conducting an excessive number of experiments. This technique helps simplify experiments by focusing on key parameters like Reynolds numbers to predict how different fluids behave under various conditions.

It's like cooking – imagine you want to create a new recipe but don’t want to make each dish from scratch. Instead, you look at what herbs and spices worked best together in other dishes (dimensionless relationships) so you can predict what you should use this time without needing to cook a hundred variations.

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