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The kinematic viscosity and specific gravity of a liquid are \(3.5 \times 10^{-4} \mathrm{m}^{2} / \mathrm{s}\) and \(0.79,\) respectively. What is the dynamic viscosity of the liquid in SI units?

Short Answer

Expert verified
The dynamic viscosity is \(0.2765 \text{ Pa} \cdot \text{s}\).

Step by step solution

01

Recall the Formula for Dynamic Viscosity

Dynamic viscosity \( \mu \) can be calculated using the formula \( \mu = u \times \rho \), where \( u \) is the kinematic viscosity and \( \rho \) is the density of the liquid. Density is related to specific gravity (SG) and the density of water (\( \rho_{water} = 1000 \text{ kg/m}^3 \)) by \( \rho = \text{SG} \times 1000 \).
02

Calculate Density from Specific Gravity

Given the specific gravity \( \text{SG} = 0.79 \), calculate the density \( \rho \) of the liquid:\[ \rho = 0.79 \times 1000 = 790 \text{ kg/m}^3 \]
03

Compute Dynamic Viscosity Using the Formula

Substitute the values \( u = 3.5 \times 10^{-4} \text{ m}^2/ ext{s} \) and \( \rho = 790 \text{ kg/m}^3 \) into the dynamic viscosity formula:\[ \mu = 3.5 \times 10^{-4} \times 790 \]Calculate:\[ \mu = 0.2765 \text{ Pa} \cdot \text{s} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Kinematic Viscosity
Kinematic viscosity is a measure of a fluid's resistance to flow under the force of gravity.
Unlike dynamic viscosity, which deals with internal friction, kinematic viscosity factors in density.
In simpler terms, kinematic viscosity tells us how fast a fluid spreads. Kinematic viscosity is calculated by the equation:- \( u = \frac{\mu}{\rho} \) where:- \( u \) is kinematic viscosity,- \( \mu \) is dynamic viscosity,- \( \rho \) is density. Typical units for kinematic viscosity are square meters per second (\( \text{m}^2/\text{s} \)).
This measure is essential for engineering and fluid mechanics as it aids in understanding the flow characteristics of various fluids under a gravitational field.
Knowing kinematic viscosity helps in designing pipelines, predicting flow rates, and assessing the fluid's stability.
Decoding Specific Gravity
Specific gravity (SG) is a dimensionless quantity that reflects how dense a substance is compared to water.
It tells us if a liquid is heavier or lighter than water, without needing any units.The formula to find specific gravity is:- \( \text{SG} = \frac{\rho}{\rho_{water}} \)where:- \( \rho \) is the density of the substance,- \( \rho_{water} \) is the water density, typically \( 1000 \text{ kg/m}^3 \).If a substance's specific gravity is less than 1, it will float on water.
If it's more than 1, it will sink.
This concept is commonly used in various industries to determine the quality and characteristics of liquids, from fuel quality assurance to alcohol content in beverages.
Demystifying Density
Density is the measure of how much mass a substance contains per unit volume.
It plays a crucial role in many scientific and engineering calculations.The formula to calculate density is:- \( \rho = \frac{m}{V} \)where:- \( \rho \) is density,- \( m \) is mass,- \( V \) is volume.Density is often expressed in kilograms per cubic meter (kg/m³).
It informs us about the compactness of a material.
High-density materials are more compact and might be heavier, while low-density materials are lighter. In fluid mechanics, understanding a fluid's density allows engineers to predict its behavior, such as buoyancy, pressure differences in a system, and the liquid's stability under flow.

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Most popular questions from this chapter

The density of a certain type of jet fuel is \(775 \mathrm{kg} / \mathrm{m}^{3}\) Determine its specific gravity and specific weight.

The kinematic viscosity of oxygen at \(20^{\circ} \mathrm{C}\) and a pressure of \(150 \mathrm{kPa}(\mathrm{abs})\) is 0.104 stokes. Determine the dynamic viscosity of oxygen at this temperature and pressure.

An important dimensionless parameter in certain types of fluid flow problems is the Froude number defined as \(V / \sqrt{g \ell}\) where \(V\) is a velocity, \(g\) the acceleration of gravity, and \(\ell\) a length. Determine the value of the Froude number for \(V=10 \mathrm{ft} / \mathrm{s}\) \(g=32.2 \mathrm{ft} / \mathrm{s}^{2},\) and \(\ell=2 \mathrm{ft} .\) Recalculate the Froude number using SI units for \(V, g,\) and \(\ell .\) Explain the significance of the results of these calculations.

An open, clean glass tube \(\left(\theta=0^{\circ}\right)\) is inserted vertically into a pan of water (see Video V1.10). What tube diameter is needed if the water level in the tube is to rise one tube diameter (due to surface tension)?

A mountain climber's oxygen tank contains 1 lb of oxygen when he begins his trip at sea level where the acceleration of gravity is \(32.174 \mathrm{ft} / \mathrm{s}^{2} .\) What is the weight of the oxygen in the tank when he reaches the top of Mt. Everest where the acceleration of gravity is \(32.082 \mathrm{ft} / \mathrm{s}^{2} ?\) Assume that no oxygen has been removed from the tank; it will be used on the descent portion of the climb.

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