Problem 19: Oil with a density of 892 kg/m is flowing smoothly through a pipe, as
shown. In the lower portion, the oil is flowing at vi = 1.84 m/s, and the pressure gauge
indicates P, = 237 kPa. In the upper portion of the pipe, oil is flowing at V2 = 3.61 m/s at a
height that is 8.63 m above the lower portion.
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onyebuchinnaji 7 months ago
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The pressure of the oil with the given properties flowing in the horizontal pipe at the upper portion of the pipe is 157 kPa.

### Pressure in the upper portion of the pipe

The pressure in the upper portion of the pipe is calculated by applying Bernoulli's equation,

P₁ + ¹/₂ρv₁² + ρgh₁ = P₂ + ¹/₂ρv₂² + ρgh₂

Given;

• P₁  = 237 kPa
• v₁ = 1.84 m/s
• h₁ = 0
• v₂ = 3.61 m/s
• h₂ = 8.63 m
• ρ = 892 kg/m³
• P₂  = ?

Susbtsitute the given parameters and solve the for the pressure in the upper portion of the pipe.

237,000 + ¹/₂(892)(1.84)² + (892)(9.8)(0) = P₂ + ¹/₂(892)(3.61)² + (892)(9.8)(8.63)

238,509.9776 = P₂ + 81,252.325

P₂ = 238,509.9776 - 81,252.325

P₂ = 157,257.65 Pa

P₂ ≅ 157 kPa

Thus, the pressure of the oil with the given properties flowing in the horizontal pipe at the upper portion of the pipe is 157 kPa.