The gauge pressure would be 2.234 ×10⁴ Pa if the pipe is changed for another twice the area.
The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
As given in the problem at some point in an underground horizontal pipe, the speed of water is 2.5m/s and the gauge pressure is 2×10⁴ Pa.
By using the continuity equation
A ₁V₁ = A₂V₂
As the area is increased to twice the original area
A ₁V₁ = 2A₁V₂
V₂ =V₁/2
=2.5 /2
=1.25 m/s
By using Bernoulli's equation
P₁ + 1/2 ρV₁² = P₂ + 1/2 ρV₂²
P₂ = 2×10⁴ + 1/2 ×1000×(2.5² -1.25²)
= 2×10⁴ + 2343.75
=22343.75 Pa
=2.234 ×10⁴ Pa
Thus, if the pipe is changed for another twice the area then the gauge pressure woul be 2.234 ×10⁴ Pa.
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