A pipe which is on a slope, transports water downwards. A doubling of cross sectional area takes place 6 above the reference level. The pressure in the smaller pipe, just before the enlargement, is 860 kPa. The flow velocity in the large pipe is 2,4 m/s. Determine the pressure in kPa at a point 1,5 m above the reference level. Ignore friction losses.

Respuesta :

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

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