Water ( = 1000 kg/m3) is flowing through a pipeline at a constant speed when it encounters a vertical bend?
Water ( = 1000 kg/m3) is flowing through a pipeline at a constant speed when it encounters a vertical bend in the pipe raising it 15.0 meters. The cross sectional area of the pipe does not change. What is the difference in pressure (PB - PA) between point A and B?
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Use Bernoulli’s equation … ½ ρ u₁ ² + ρ g y₁ + p₁ = ½ ρ u₂ ² + ρ g y₂ + p₂
… flowing through the pipeline at constant speed … u₁ = u₂ … so that the
above equation reduces to …
… p₂ - p₁ = ρ g ( y₁ - y₂ ) = - ρ g ( y₂ - y₁ )
……………………………. = - ( 1000 kg / m ³ ) ( 9.8 m / s ² ) ( 15 m ) = 1.47 × 10 ⁵ Pa
……………………………. = - 1.47 × 10 ⁵ Pa ...
Pressure at the higher level is lower …