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A fluid of density rho = 900 kg/m3 flows along a pipe of constant diameter from point A to point B. Gauge pressure at point A is equal to zero, and absolute pressure at point B is 30% lower than pressure at point A. What is the height difference, Δh, between points A and B?
a. Δh = 8.09 m with point A above point B.
b. Δh = 344 m with point B above point A.
c. Δh = 303 m with point B above point A.
d. Δh = 3.44 m with point A above point B.

Respuesta :

batolisis

The height difference between points A and B is : ( B ) Δh = 3.44 m with point B above point A.

Given data :

fluid density = 900 kg/m³

Diameter of pipe = constant

Gauge pressure at Point A = 0

Gauge pressure at point B = 30% lower

Determine the height difference between points A and B

first step : determine absolute pressure

Pa (absolute pressure )= gauge pressure + atmospheric pressure

                                      = 0 + patm

Therefore : Pa = Patm

Also;

Pressure at point B ( Pb ) = Pa - 30%Pa

                                          = 0.7 Patm

Hence ; Pa - Pb = 0.3 Patm ----- ( 1 )

Final step : Determine the height difference

we will apply the formula below from equation ( 1 )

p *g * Δh = 0.3 * 1.013 * 10⁵      ( note : Patm = 1.013 * 10⁵ )

900 * 9.81 * Δh = 0.3 * 1.013 * 10⁵

therefore :

Δh = ( 0.3 * 1.013 * 10⁵ ) / ( 900 * 9.81 )

     = 3.44 m

Hence we can conclude that The height difference between points A and B is Δh = 3.44 m with point B above point A.

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