Answer:
P₂ = 830.75 kPa
Explanation:
Given:
Pressure in the smaller pipe,P₁ = 860 kPa
Velocity in the larger pipe, v₂ = 2.4 m/s
Therefore velocity in the smaller pipe, v₁ = 4.8 m/s ( velocity gets doubled since area is reduced to half )
Height at section where the area is doubled, z₁ = 6 m
Height at the section where pressure is to be calculated, z₂ = 1.5 m
Now apply Bernouli Equation between the section of enlargement and at section where pressure is to be calculated,
[tex]\frac{P_{1}}{\rho .g}+\frac{v_{1}^{2}}{2.g}+z_{1} = \frac{P_{2}}{\rho .g}+\frac{v_{2}^{2}}{2.g}+z_{2}[/tex]
[tex]\frac{860}{1000 \times 9.81}+\frac{4.8^{2}}{2\times 9.81}+6 = \frac{P_{2}}{1000 \times 9.81}+\frac{2.4^{2}}{2\times 9.81}+1.5[/tex]
P₂ = 830.75 kPa
Therefore, pressure at the section 1.5 m above datum is 830.75 kPa