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Answer:
Yes equation is valid.
Explanation:
Given:
h = (0.04 to 0.09)(D/d)^4*V^2/2*g
Using SI units to assign dimensions to every quantity as follows:
Energy loss per unit weight h = J / N = kg m ^2 s^-2 / kg m s^-2 = [m]
Hose diameter D = [m]
Nozzle tip diameter d = [m]
Fluid velocity in the hose V = [ m s^-1 ]
Acceleration of gravity g = [ m s^-2 ]
Using the Given Equation and plug the SI units of respective quantities:
h = (0.04 to 0.09)(D/d)^4*V^2/2*g
[m] = (0.04 to 0.09)([m] / [m])^4*[ m s^-1 ]^2/2*[ m s^-2 ]
Simplify the equation above:
[m] = ( 1 )^4 * [ m^2 s^-2 ] / [ m s^-2 ]
[m] = [m]
Hence, SI units of RHS of given equation = LHS of given equation, we can say the equation has consistent dimensions.
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Answer: Pi= 4 - 4/3 + 4/5 - 4/7 + 4/9 ...
Explanation:
Is the same as the example,
If Π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 ...
Then
(Π/4 )*4= 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 ...)
Π =4 - 4/3 + 4/5 - 4/7 + 4/9 ...
The way to write this is
Sum(from n=0 to n=inf) of (-1)^n 4/(2n+1)
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