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Shtirlitz [24]
3 years ago
8

The three components of velocity in a velocity field are given by u = Ax + By + Cz, v = Dx + Ey + Fz, and w = Gx + Hy + Jz. Dete

rmine the relationship among the coefficients A through J that is necessary if this is to be a possible incompressible flow field.
Physics
1 answer:
Alexxandr [17]3 years ago
6 0

Answer:

The relationship is only between the coefficients A, E and J which is:

A + E + J = 0. The remaining coefficients can be anything without any constraints.

Explanation:

Given:

The three components of velocity is a velocity field are given as:

u = Ax + By + Cz\\\\v = Dx + Ey + Fz\\\\w = Gx + Hy + Jz

The fluid is incompressible.

We know that, for an incompressible fluid flow, the sum of the partial derivatives of each component relative to its direction is always 0. Therefore,

\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0

Now, let us find the partial derivative of each component.

\frac{\partial u}{\partial x}=\frac{\partial }{\partial x}(Ax+By+Cz)\\\\\frac{\partial u}{\partial x}=A+0+0=A\\\\\frac{\partial v}{\partial y}=\frac{\partial }{\partial y}(Dx+Ey+Fz)\\\\\frac{\partial v}{\partial y}=0+E+0=E\\\\\frac{\partial w}{\partial z}=\frac{\partial }{\partial z}(Gx+Hy+Jz)\\\\\frac{\partial w}{\partial z}=0+0+J=J

Hence, the relationship between the coefficients is:

A+E+J=0

There is no such constraints on other coefficients. So, we can choose any value for the remaining coefficients B, C, D, F, G and H.

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Consider three identical electric bulbs of power P. Two of bulbs are connected in series and the third one is connected in paral
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Answer: 3P/2

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( as the voltage remains same in parallel circuit)

we can calculate the Current across both circuits

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Power1=Voltage * Current1

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Power2=V*\frac{V}{2R} \\Power2=\frac{V^2}{2R} \\Power2=P/2

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6 0
3 years ago
The equatorial diameter of venus is 7,523 miles. if a mile equals 1.609 km, what is venus's diameter in kilometers?
polet [3.4K]

The diameter of venus in km is 12104.507Km.

<h3 /><h3>What is Unit conversion?</h3>

By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units. The act of converting something from one form to another in mathematics, such as from inches to millimetres or from litres to gallons, is known as conversion.

the diameter of venus = 7,523 miles

1 mile = 1.609 km

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diameter of venus = 7523 × 1.609 Km

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2 years ago
A bicyclist travels in a circle of radius 30.0 m at a constant speed of 8.00 m/s. the bicycle-rider mass is 82.0 kg calculate ne
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3 years ago
As light shines from air to water, the index of refraction is 1.02 and the angle of incidence is 38.0 °. What is the light's an
muminat

Answer:

Light's angle of refraction = 37.1° (Approx.)

Explanation:

Given:

Index of refraction = 1.02

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Angle of incidence = 38°

Find:

Light's angle of refraction

Computation:

Using Snell's law;

Sin[Angle of incidence] / Sin[Light's angle of refraction] = Index of refraction / Base of refraction

Sin38 / Light's angle of refraction = 1.02 / 1

Sin[Light's angle of refraction] = Sin 38 / 1.02

Sin[Light's angle of refraction] = [0.6156] / 1.02

Sin[Light's angle of refraction] = 0.6035

Light's angle of refraction = 37.1° (Approx.)

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3 years ago
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