Find the gauge pressure at a second point in the line, 11.0m lower than the first, if the pipe diameter at the second point is twice that at the first.

Incomplete question.The complete question is here

At one point in a pipeline the water’s speed is 3.00 m/s and the gauge pressure is 5.00×10⁴Pa.Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

P₂=1.62×10⁵ Pa

Explanation:

Given Data

Pressure=5.00×10⁴Pa

Water Speed= 3.0 m/s

Length= 11.0 m

To find

Pressure at a second point in the line

Solution

Apply Bernoulli equation at two points

Continuity equation P₁A₁=P₂A₂

As we have to find P₂.So

P₂=(P₁A₁)/A₂

And

V₁=1/A

So

P₂=P₁+1/2ρ(V₁²-V₂²)+ρg(y₁-y₂)

P₂=P₁+ρ{15/32V₁²+g(y₁-y₂)}

P₂=5.00×10⁴Pa+(1.00×10³ kg/m³){15/(3.00)²+9.8(11 m)}

P₂=1.62×10⁵ Pa

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