The gauge pressure of the pipe is 2.234 ×10⁴ Pa, if the pipe is changed for another twice the area.
To find the gauge pressure the values given are,
speed of water = 2.5 m/s
Gauge pressure = 2×10⁴ Pa
<h3>What is pressure?</h3>
Definition:
Pressure can be defined as the total applied force per unit of area. The pressure depends both on externally applied force as well the area on which it is applied.
To find the gauge pressure first we have use continuity equation,
A ₁V₁ = A₂V₂
By the given condition: As the area is increased to twice the original area
A ₁V₁ = 2A₁V₂
A₁ gets cancelled on both the sides,
V₂ =V₁/2
=2.5 /2
V₂=1.25 m/s
Then, substituting the values in Bernoulli's equation,
Equation is given as,
P₁ + 1/2 ρV₁² = P₂ + 1/2 ρV₂²
Taking 1/2 ρ as common,
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 is 2.234 ×10⁴ Pa.
Learn more about pressure,
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