the pressure in a water pipe in the basement of an apartment house is 4.10 x 10^

Question

the pressure in a water pipe in the basement of an apartment house is 4.10 x 10^5 Pa, but on the seventh floor is only 1.85 x 10^5 Pa. draw a diagram of the floor plan and determine the height between the basement and the seventh floor? explain the principle and state if you made any assumptions to solve the problem

2. consider h- atom. using Coulomb's law show that the speed of the electron is 2.19 x 10^6 m/s given that the radius of electrons orbit is .0529 nm (use knowledge if uniform circular motion)

Explanation / Answer

P = DGH where P = pressure; D = density of the fluid;

 G = 9.81 m/s^2; H = height of fluid above point of interest

Pb = pressure at basement level; P7 = pressure at seventh floor

Pb - P7 = DG(Hb) - DG(H7) where Hb = height of fluid above basement;

 H7 = height of fluid above seventh floor

4.10E5 Pa - 1.85E5 Pa = DG(Hb - H7) = (1.0E3 kg/m^3)(9.81 m/s^2)(Hb - H7)

2.25E5 = 9.81E3(Hb - H7)

Hb - H7 = 22.9 meters

equate centripetal force with coulomb force between two point charges.

mv ²/r = Ze ²/4πεr ² and solve for r to get:

r = Ze ²/4πεmv ²

You are given the equation, mvr = nh/2Ï€, solve for r to get:

r = nh/2Ï€mv

equate both r together to get:

Ze ²/4πεmv ² = nh/2Ï€mv

solve for v

v = Ze ²/2εnh

Z=1 in hydrogen so:

v = (1.6x10^-19) ²/[2(8.85x10^-12)(1)(6.63x10…

v = 2.18x10^6 m/s

Using a relativistic approach yields a similar answer that's why a non-relativistic approach is justified.

v = γv'

v = 2.18x10^6/[√(1-2.18x10^6/3x10^8)]

v = 2.19x10^6 m/s

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