Water is flowing smoothly through a closed pipe system. At one point the speed of water is 3m s⁻¹ while at another point 3 m higher, the speed is 4 m s⁻¹. If the pressure is 80 kPa at the lower point what is the pressure at the upper end? (Ans: 47 kPa)



Data Given:


Velocity at lower point  = v₁ = 3 m s⁻¹

Velocity at upper point  = v₂ = 4 m s⁻¹

Pressure at lower point  = P₁ = 80 kPa = 80000 Pa

Difference in height = h₂ - h₁ = 3 m 

value of g = 9.8 m s⁻² 

Density of water = ⍴ = 1000 kg m⁻³


To Find:


Pressure at lower point  = P₂ = ?


Solution:


By using the formula Bernoulli's equation


P₁ + `\frac {1}{2}`⍴v₁² + ⍴gh₁ =  P₂ + `\frac {1}{2}`⍴v₂² + ⍴gh₂  

P₁ + `\frac {1}{2}`⍴v₁² - `\frac {1}{2}`⍴v₂² + ⍴gh₁ - ⍴gh₂   =  P₂ 

or

P₂ = P₁ + `\frac {1}{2}`⍴ (v₁²- v₂²) - ⍴g (h₂ - h₁)


By putting values

P₂ = 80000 Pa + `\frac {1}{2}` ｘ 1000 kg m⁻³ ((3 m s⁻¹)²- (4 m s⁻¹)²) - 1000 kg m⁻³ ｘ9.8 m s⁻² ｘ (3 m)

P₂ = 80000 Pa + 500 kg m⁻³ (9 m² s⁻²- 16 m² s⁻²) - 29400 kg m⁻¹ s⁻²

P₂ = 80000 Pa + 500 kg m⁻³ (-7 m² s⁻²) - 29400 kg m⁻¹ s⁻²

P₂ = 80000 Pa - 3500 kg m⁻¹ s⁻² - 29400 kg m⁻¹ s⁻²

As Pa = kg m⁻¹ s⁻²

P₂ = 80000 Pa - 3500 Pa - 29400 Pa

P₂ = 47100 Pa

P₂ = 47.100 ｘ10³ Pa

or

P₂ = 47.1 kPa -----------------Ans.



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.