Calculate the Reynolds numbers for the flow of water and for air through a 4-mm-diameter tube, i

Calculate the Reynolds numbers for the flow of water and for...

Key Concepts

Flow Regime Classification

Flow regime classification refers to determining whether a fluid flow is laminar, turbulent, or transitional based on the Reynolds number. Low Reynolds numbers indicate laminar flow where the motion is orderly and parallel, while high Reynolds numbers suggest turbulent flow characterized by random and chaotic fluid movement. This classification is fundamental to predicting flow behavior, energy losses, and designing fluid systems.

Characteristic Length

The characteristic length is a representative physical dimension used in the calculation of the Reynolds number. In the case of flow through a tube, the tube’s diameter is typically considered the characteristic length. This parameter helps in relating the geometric features of the system to the flow dynamics.

Fluid Properties (Density and Viscosity)

Fluid properties such as density and viscosity play a key role in determining the Reynolds number. Density measures the mass per unit volume of the fluid, while viscosity quantifies the fluid's resistance to deformation and flow. Their values, which can vary with temperature and pressure, are essential for accurately assessing the behavior of the fluid under flow conditions.

Reynolds Number

The Reynolds number is a dimensionless parameter used to predict the flow regime in fluid mechanics. It relates inertial forces to viscous forces and is calculated using parameters such as velocity, characteristic length, and fluid properties like density and viscosity. This concept is crucial for determining whether the flow will be laminar, turbulent, or in transition.

Transcript

00:03 So in this question what we are given is that we are given a tube, right? and it's the the tube's diameter is equal to diameter is equal to 4 millimeter.

00:20 Right.

00:21 And the mean velocity, mean velocity, it's equal to 3 meter per second.

00:32 Right the temperature is equal to 30 degree centigrade right and we are as per the question statement right so we assume that the air is at standard atmospheric atmospheric pressure p right now what we need to find out in this question is to calculate calculate the reynolds number right the reynolds number for the flow of water and for air right so for the let's say that the a part is for the flow of water and the b part is for inner right so the solution for this question right it's very easy so let's start with it.

01:52 Now, first of all, what we have over here is that what we need to find out over here is the values of the dynamic viscosity, right? we need to find these values for both water and air, right? so let the dynamic viscosity for water be meal.

02:22 Sub w right and the dynamic viscosity for a let it be mu sub a right so what we're going to do is that we are going to look the table for the values right at temperature that is 30 degrees centigrade and it's given right afterwards what we are going to do is that density of air at the given temperature at the given temperature will be calculated from the ideal gas law right so we have be standard right pressure standard right so that is equal to the density of air into r times t right so if we solve it for the density right so we get that if we solve this equation so we get that row sub a it's equal to the standard pressure divided by r times t right so the value of r for this case it's equal to 303 .3 .15 calvins right and sorry that is the temperature sticks this is the temperature right and r is equal to 287 .05 jule per kilogram galvan right now now as you can see that the given temperature was in decrease centigrade but we have converted into calvin.

04:03 Right.

04:03 So what we need to do is that we are going to substitute these values over here.

04:07 Right.

04:07 You should know the static atmospheric pressure and that is 101, 325 bascels, right? so just plug it in over here and we get at the value of the density.

04:24 It's equal to 1 .16...

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