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An application of Bernoulli's equation for fluid flow is found in (a) Dynamic lift of an aeroplane (b) Viscosity meter (c) Capillary rise (d) Hydraulic press

Short Answer

Expert verified
Dynamic lift of an aeroplane is described by Bernoulli's equation.

Step by step solution

01

Understanding Bernoulli's Principle

Bernoulli's principle states that for an incompressible, non-viscous fluid, the total mechanical energy (sum of the pressure energy, kinetic energy, and potential energy) along a streamline is constant. It is mathematically expressed as\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]where \( P \) is the pressure, \( \rho \) is the fluid density, \( v \) is the flow speed, and \( h \) is the height above some reference point. This principle applies to scenarios involving fluid flow and pressure changes.
02

Analyze Each Option with Respect to Bernoulli’s Equation

We need to evaluate each option related to the application of fluid flow dynamics: - (a) Dynamic lift of an aeroplane: This involves air pressure differences on the top and bottom surfaces of the wings due to varying speeds, exactly modeled by Bernoulli's equation. - (b) Viscosity meter: This uses viscosity measurement rather than Bernoulli's principle which involves pressure differences without viscosity considerations. - (c) Capillary rise: Deals with liquid rise in narrow tubes due to surface tension, not governed by Bernoulli’s equation. - (d) Hydraulic press: Operates on Pascal’s law of pressure transmission, not Bernoulli’s principle.
03

Identify the Correct Application

From the analysis, the dynamic lift of an aeroplane (option a) is directly explained by Bernoulli's equation as it involves pressure differences and varying velocities that affect lift. This is an application of Bernoulli's principle because the fluid (air) speeds differ across the aeroplane's wings, changing the pressure and thus creating lift.

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Key Concepts

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

Fluid Dynamics
Fluid dynamics is a fascinating branch of physics that focuses on the movement of fluids, which can be either liquids or gases. It aims to understand how these fluids behave when they are in motion or at rest. By studying fluid dynamics, we can predict the behavior of air, water, and other fluids in various situations, ranging from simple flow in a pipe to complex atmospheric phenomena.
  • Pressure: One of the key aspects of fluid dynamics is pressure. Pressure can vary with position in any fluid, influencing how the fluid moves.
  • Density: It's important to note that fluid density plays a critical role in determining how a fluid behaves under different conditions.
  • Velocity: The speed and direction at which the fluid flows is another crucial factor.
Bernoulli's Principle is a cornerstone of fluid dynamics, highlighting how the speed of a fluid impacts pressure and height. This principle is particularly useful in many engineering applications, such as designing airplane wings, predicting weather patterns, and even understanding how blood flows through arteries.
Aerodynamic Lift
Aerodynamic lift is an essential force that enables objects, such as airplanes, to fly. It occurs due to the pressure difference on the wings' surfaces. When an airplane moves, air flows over and under its wings at different speeds. According to Bernoulli's Principle, faster airflow results in lower pressure. As the airplane progresses forward:
  • Air above the wing surface moves faster than the air below,
  • This creates a pressure difference,
  • Resulting in a net upward force called lift.
Not only is aerodynamic lift crucial for airplanes, but it's also a vital factor for many other structures, such as bridges and wind turbines, to ensure stability and efficiency. By manipulating wing shape and angle, engineers can optimize the lift for different flight conditions.
Streamline Flow
Streamline flow, also known as laminar flow, is a type of fluid motion where every particle follows a smooth path. These paths, or streamlines, are parallel and don’t intersect. Streamline flow is characterized by constant speed and layer consistency, meaning it occurs quietly without turbulence. Streamline flow is relevant in both natural phenomena and engineering applications. In this flow type:
  • Fluid layers move steadily past each other,
  • Maintaining a consistent path and velocity,
  • Results in minimal energy loss due to resistance.
Designing systems for streamline flow is crucial for efficient fluid transportation, minimizing energy costs, and reducing mechanical wear. Understanding and predicting streamline flow involve solving complex equations, but grasping its basic principles helps in practical applications like pipe design, airfoil shaping, and smoke trail analysis.

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Most popular questions from this chapter

When equal volumes of two substances are mixed, the specific gravity of mixture is \(4 .\) When equal weights of the same substances are mixed, the specific gravity of the mixture is \(3 .\) The specific gravity of the two substances would be (a) 6 and 2 (b) 3 and 4 (c) \(2.5\) and \(3.5\) (d) 5 and 3

A cart supports a cubic tank filled with a liquid upto the top. The cart moves with a constant acceleration a in the horizontal direction. The tank is tightly closed. Assume that the lid does not exert any pressure on the liquid when in motion with uniform acceleration. The pressure at a point at a depth \(h\) and distance \(l\) from the front wall is (a) \(d g h\) (b) dla (c) \(d g h+d l a\) (d) \(d g h-d l a\)

If the terminal speed of a sphere of gold (density \(=19.5\) \(\mathrm{kg} / \mathrm{m}^{3}\) ) is \(0.2 \mathrm{~m} / \mathrm{s}\) in a viscous liquid \(\left(\right.\) density \(\left.=1.5 \mathrm{~kg} / \mathrm{m}^{3}\right)\) find the terminal speed of a sphere of silver (density = \(10.5 \mathrm{~kg} / \mathrm{m}^{3}\) ) of the same size in the same liquid (a) \(0.2 \mathrm{~m} / \mathrm{s}\) (b) \(0.4 \mathrm{~m} / \mathrm{s}\) (c) \(0.133 \mathrm{~m} / \mathrm{s}\) (d) \(0.1 \mathrm{~m} / \mathrm{s}\)

In which one of the following cases will the liquid flow in a pipe be most streamlined? (a) Liquid of high viscosity and high density flowing through a pipe of small radius (b) Liquid of high viscosity and low density flowing through a pipe of small radius (c) Liquid of low viscosity and low density flowing through a pipe of large radius (d) Liquid of low viscosity and high density flowing through a pipe of large radius

A vessel contains oil (density \(=0.8 \mathrm{gm} / \mathrm{cm}^{3}\) ) over mercury (density \(\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)\). A homogeneous sphere floats with half of its immersed in mercury and the other half in oil. The density of the material of the sphere in \(\mathrm{g} / \mathrm{cm}^{3}\) is (a) \(3.3\) (b) \(6.4\) (c) \(7.2\) (d) \(12.8\)

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