Ask Question
11 June, 13:42

Determine the flow velocities at the inlet and exit sections of an

inclined tapering pipe using fluid flow theory and given pressure

readings and flow rates.

There is a sloping pipeline that has one end 1.35 m higher than the

other. The pipe section tapers from 0.95 m diameter at the top end to

0.44m diameter at the lower end. The difference in pressure between

the two sections is 12.35kPa, with pressure being greater at higher

level.

Your task is to determine the inlet and exit velocities and the

volume

flow rate of the inclined pipe.

+2
Answers (1)
  1. 11 June, 14:20
    0
    The inlet velocity v₁ = 6.66 m/s, the exit velocity v₂ = 7.32 m/s and the volume flow rate Q = 4.72 m³/s

    Explanation:

    Using Bernoulli's equation

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

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

    ΔP + ρgΔh = 1/2ρ (v₂² - v₁²) (1)

    where ΔP = pressure difference = 12.35 kPa = 12350 Pa

    Δh = height difference = 1.35 m

    From the flow rate equation Q = A₁v₁ = A₂v₂ and v₁ = A₂v₂/A₁ = d₂²v₂/d₁² where v₁ and v₂ represent the inlet and exit velocities from the pipe and d₁ = 0.95 m and d₂ = 0.44 m represent the diameters at the top end and lower end of the pipe respectively.

    Substituting v₁ into (1), we have

    ΔP + ρgΔh = 1/2ρ (v₂² - (d₂²v₂/d₁²) ²)

    ΔP + ρgΔh = 1/2ρ (v₂² - (d₂/d₁) ⁴v₂²)

    v₂ = √[2 (ΔP + ρgΔh) / ρ (1 - (d₂/d₁) ⁴) }

    substituting the values of the variables, we have

    v₂ = √[2 (12350 Pa + 1000 kg/m³ * 9.8 m/s² * 1.35 m) / (1000 kg/m³ (1 - (0.44 m/0.95 m) ⁴)) }

    = √[2 (12350 Pa + 13230 Pa) / (1000 kg/m³ * 0.954) ]

    = √[2 (25580 Pa) / 954 kg/m³]

    = √[51160 Pa/954 kg/m³]

    = √53.627

    = 7.32 m/s

    v₁ = d₂²v₂/d₁²

    = (0.44 m/0.95 m) ² * 7.32 m/s

    = (0.954) ² * 7.32 m/s

    = 6.66 m/s

    The volume flow rate Q = A₁v₁

    = πd₁²v₁/4

    = π (0.95 m) ² * 6.66 m/s : 4

    = 18.883 m³/s : 4

    = 4.72 m³/s

    So, the inlet velocity v₁ = 6.66 m/s, the exit velocity v₂ = 7.32 m/s and the volume flow rate Q = 4.72 m³/s
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Determine the flow velocities at the inlet and exit sections of an inclined tapering pipe using fluid flow theory and given pressure ...” in 📙 Engineering if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers