Table of Contents
- 1 How do you derive spherical coordinates?
- 2 How do you derive continuity equations from spherical coordinates?
- 3 How do you convert continuity to cylindrical coordinates?
- 4 How do you derive Bernoulli’s equation?
- 5 How do you derive continuity equations?
- 6 How do you derive Bernoulli’s equation from Euler?
- 7 What are the coordinates of a sphere?
- 8 What is a spherical coordinate system?
How do you derive spherical coordinates?
Starts here5:04Deriving Spherical Coordinates (For Physics Majors) – YouTubeYouTubeStart of suggested clipEnd of suggested clip60 second suggested clipAnd Z. Now this corresponds to being able to specify. Where a point in space is by going someMoreAnd Z. Now this corresponds to being able to specify. Where a point in space is by going some distance in the X Direction. Some distance in the Y direction. And then some distance in the Z Direction.
How do you derive continuity equations from spherical coordinates?
Starts here15:05Equation of continuity in spherical polar coordinates – YouTubeYouTubeStart of suggested clipEnd of suggested clip52 second suggested clipInto Q theta. Plus 1 upon R sine square theta. Then by Del Phi. Of Rho Q Phi will be equal to 0MoreInto Q theta. Plus 1 upon R sine square theta. Then by Del Phi. Of Rho Q Phi will be equal to 0 which is desired equation of continuity. And spherical coordinates thanks for watching.
How do you convert latitude and longitude to spherical coordinates?
To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2).
How do you convert continuity to cylindrical coordinates?
Starts here10:18Deriving Continuity Equation in Cylindrical Coordinates – YouTubeYouTube
How do you derive Bernoulli’s equation?
We also assume that there are no viscous forces in the fluid, so the energy of any part of the fluid will be conserved. To derive Bernoulli’s equation, we first calculate the work that was done on the fluid: dW=F1dx1−F2dx2=p1A1dx1−p2A2dx2=p1dV−p2dV=(p1−p2)dV.
How do you write an equation in cylindrical coordinates?
Starts here6:40Write a Rectangular Equations in Cylindrical Form – YouTubeYouTube
How do you derive continuity equations?
Derivation Of Continuity Equation
- The continuity equation is defined as the product of cross-sectional area of the pipe and the velocity of the fluid at any given point along the pipe is constant.
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- Δx1 = v1Δt.
- V = A1 Δx1 = A1 v1 Δt.
- Δm1= Density × Volume.
- => Δm1 = ρ1A1v1Δt ——–(Equation 1)
How do you derive Bernoulli’s equation from Euler?
Starts here11:16Bernoulli’s equation derivation from Euler’s equation of motion – YouTubeYouTube
How to convert to spherical coordinates?
Here are the conversion formulas for spherical coordinates. x = ρsinφcosθ y = ρsinφsinθ z = ρcosφ x2+y2+z2 = ρ2 x = ρ sin
What are the coordinates of a sphere?
In mathematics and physics, spherical polar coordinates (also known as spherical coordinates) form a coordinate system for the three-dimensional real space . Three numbers, two angles and a length specify any point in . The two angles specify the position on the surface of a sphere and the length gives the radius of the sphere.
What is a spherical coordinate system?
Spherical coordinate system. A spherical coordinate system, with origin O and azimuth axis A. The point has radius r = 4, elevation θ = 50°, and azimuth φ = 130°.
What are the coordinates of the celestial sphere?
The Celestial Sphere : We can locate any object on the celestial sphere by giving it two coordinates, called the Right Ascension and the Declination . These are called celestial coordinates. Analogous to the longitude on Earth, the Right Ascension of an object on the celestial sphere is measured along the celestial equator,…