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Fluid Mechanics Homework Help

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About Fluid Mechanics

What is fluid mechanics?

Fluid mechanics is an important branch of physics that deals with the behavior of fluids (gases, liquids, blood, and plasmas) due to the forces on them. Fluid statics, which studies fluids at rest, and fluid dynamics, which studies fluid motion under the effect of forces, are its two subdivisions.

Its parent subject, continuum mechanics, models matter macroscopically rather than microscopically. Consequently, it doesn’t take the atomic view of matter into account. Fluid mechanics, particularly fluid dynamics, are typically mathematically complex and involve numerical methods, often involving computers. A relatively recent discipline, computational fluid dynamics (CFD), is engaged in this calculational approach. The visual nature of fluid flow has given rise to particle image velocimetry, an experimental subject for analyzing and visualizing fluid flow.

Fluid mechanics is a part of many engineering and non-engineering disciplines, including chemical, mechanical, biomedical, and civil engineering, oceanography, geophysics, meteorology, biology, and astrophysics.

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Topics in fluid mechanics

The common topics students study in introductory fluid mechanics are:

  • Types of fluids
  • Shear stress
  • Viscosity
  • Non-Newtonian fluids
  • Kinematic viscosity
  • Viscosity of mixtures
  • Fluid density
  • Bulk modulus
  • Surface tension

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Fundamentals of fluid mechanics

The elementary fluid mechanics principles are:

  • The energy equation.
  • The momentum principle (or conservation of momentum).
  • The continuity equation (i.e., conservation of mass).

The Bernoulli equation is a closely related concept derived from the motion equation.

Momentum principle

The momentum principle states that a change of momentum in a system results from all forces acting on the system. For the flow of fluids, those forces could be; weight in the downstream direction, pressure in the downstream direction, friction in the upstream direction, and pressure in the upstream direction.

Continuity equation

The continuity equation states that the fluid’s volume or flow rate at any point while it flows through a pipe, is constant. The flow rate or volume flow per second is the product of the fluid’s velocity and the pipe’s cross-sectional area at the given point. The continuity equation formula is:

R = v x A = constant


R is the flow rate (volume)

v is the fluid’s velocity

A is the pipe’s cross-sectional area

The continuity equation assumes the following points:

  • The tube has a non-viscous fluid flowing in it
  • The tube has a single entry and a single exit
  • The flow is steady and incompressible

Energy equation

The First Law of Thermodynamics gave rise to the energy equation. It involves energy, heat transfer, and work. We often use the energy equation for incompressible flow problems. The mechanical energy equation is analogous to an extended version of the Bernoulli equation as it, with some limitations, works in the same way as the Bernoulli Equation.

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Bernoulli’s equation

In fluid dynamics, it states that a decrease in the fluid’s potential energy or static pressure causes an increase in the flow speed of a fluid and vice-versa. Daniel Bernoulli published it in 1738 in his book Hydrodynamica. It only applies to isentropic flows: when the effects of non-adiabatic processes (like heat radiation) and irreversible processes (e.g., turbulence) are small enough so that they aren’t significant enough.

Various kinds of fluid flow result in different forms of Bernoulli’s equation. The elementary form of Bernoulli’s equation applies to incompressible flows (e.g., most liquids and gases moving at speeds of a low Mach number). Compressible fluids flowing at higher Mach numbers comply with the equation’s advanced forms.

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Dimensional analysis in fluid mechanics

The main attraction of dimensional analysis is its versatility. It is helpful for elementary equations and complex system analysis problems. For complex systems, fluid mechanics uses formal dimensional analysis of multiple attributes or characteristics in methods with well-defined paradigms and a systematic approach. The Buckingham 𝛑 Model is one of the most widely applicable models, and another one is the three-step Rayleigh method.

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