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Hydrodynamics

Hydrodynamics is a subset of fluid dynamics which studies liquids that are at rest or in motion. Fluid mechanics has been around for thousands of years. Archimedes made the first known contributions with his invention of the screw pump. The ancient Romans developed extensive hydraulic machines and devices by using Archimedes’ screw pump and mine pumping system.

Major developments in hydrodynamics did not start to happen until Sir Isaac Newton formulated the laws of motion. Leonhard Euler applied these laws to fluids. He recognized that dynamic laws for fluids could only be expressed with relatively simple forms. The effects of friction or viscosity had to be neglected. Thus, the results of his analysis were only an estimate.

Today, we have a series of equations to explain the properties of liquids through the conservation laws of mass, energy and momentum. Hydrodynamics is largely used to explain flow through pipes and various obstacles, such as dams. It is also used to predict the flow patterns of turbulent or interrupted flow. With computational simulations, large hydrodynamic problems can be simulated on a small scale. This is extremely useful when looking at the conditions in the ocean or large bodies of water.

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Non-viscous flow of water due to pressure difference

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Underwater Jet Dispersal Rates

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The Viscosity of Water Using the Capillary Method

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Hydrostatics and Hydrodynamics: Pressure and Bernoulli Equation

Please show all the work. Water is flowing upward in the vertical duct as shown (in the figure in the attachment). The velocity at the inlet (station 1) is 100 ft/s, and the area ratio between station 1 and 2 is 0.6 (A2/A1 = 0.6). Two pressure taps, 10 ft apart, are connected to a differential manometer, as shown. The specif

Set of Ten Problems on Hydrodynamics

(See attached file for full problem description).

Hydrodynamics: Equation of continuity, rate of flow of fluid

Q: A meter long hose of 14cm diameter is connected to a second hose which is 4 meters long and 7cm in diameter. At the open end of the second hose water flows out at a rate of 8 cm^3/sec. What is the ratio of the speed of the water flowing in the second hose to the speed of the water flowing in the first hose?

Hydrodynamics: Bernoulli's equation and fluid flow,

If for the pipe carrying water in a building, h = 144 meters, v1 = 2.88 m/s, and the cross-sectional area at 1 is twice that at 2, what must P1 be, to the nearest K Pa, in order that P2 = 101000 Pa?

Problems

For each topic describe in a brief paragraph 1) Its key characteristics and 2) A personal observation, or an experience with, or an example of a real world application of the topic. A) water pressure b) fluids in motion c) Bernoulli's equation d) Archimedes' principle

Euler Equation of Hydrodynamics

Start from Euler's equation ... Take the divergence to obtain delta-p as a quadratic expression in ... Use divv = 0 to make this as simple as you can. Assuming v and p vanish sufficiently rapidly at 1, express p itself in terms of v alone.