Question

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.

Answer 1

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.

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