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    Labrotary Work 1

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    kevin loachamin
    1. The document describes a laboratory experiment using Bernoulli's equation to analyze the flow of an incompressible liquid through a pipe with varying diameter and height. 2. Key variables like pressure, velocity, height, and area were measured at different points along the pipe to calculate the specific energy and energy losses using Bernoulli's equation. 3. The conclusion is that Bernoulli's equation can be used to describe how properties of a fluid like pressure and velocity change along a streamline depending on factors like pipe area, demonstrating the conservation of energy for an incompressible fluid.

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    Labrotary Work 1

    Uploaded by

    kevin loachamin
    40 views4 pages
    1. The document describes a laboratory experiment using Bernoulli's equation to analyze the flow of an incompressible liquid through a pipe with varying diameter and height. 2. Key variables like pressure, velocity, height, and area were measured at different points along the pipe to calculate the specific energy and energy losses using Bernoulli's equation. 3. The conclusion is that Bernoulli's equation can be used to describe how properties of a fluid like pressure and velocity change along a streamline depending on factors like pipe area, demonstrating the conservation of energy for an incompressible fluid.

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    Hydraulic

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    Labrotary work 1

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    1. The document describes a laboratory experiment using Bernoulli's equation to analyze the flow of an incompressible liquid through a pipe with varying diameter and height. 2. Key variables like pressure, velocity, height, and area were measured at different points along the pipe to calculate the specific energy and energy losses using Bernoulli's equation. 3. The conclusion is that Bernoulli's equation can be used to describe how properties of a fluid like pressure and velocity change along a streamline depending on factors like pipe area, demonstrating the conservation of energy for an incompressible fluid.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    40 views4 pages

    Labrotary Work 1

    Uploaded by

    kevin loachamin
    1. The document describes a laboratory experiment using Bernoulli's equation to analyze the flow of an incompressible liquid through a pipe with varying diameter and height. 2. Key variables like pressure, velocity, height, and area were measured at different points along the pipe to calculate the specific energy and energy losses using Bernoulli's equation. 3. The conclusion is that Bernoulli's equation can be used to describe how properties of a fluid like pressure and velocity change along a streamline depending on factors like pipe area, demonstrating the conservation of energy for an incompressible fluid.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 4

    National Aerospace University – "Kharkiv Aviation Institute"

    Department of Aerohydrodynamics

    LABORATORY WORK №1
    Specific energy of a flowing liquid
    Bernoulli’s equation.
    Consider a pipe with varying diameter and height through which an
    incompressible fluid is flowing. The relationship between the areas of cross-
    sections A, the flow speed v, height from the ground y, and pressure p at two
    different points 1 and 2 is given in the figure below.

    Assumptions:
     The density of the incompressible fluid remains constant at both points.
     The energy of the fluid is conserved as there are no viscous forces in the
    fluid.
    Therefore, the work done on the fluid is given as:
    dW = F1dx1 – F2dx2
    dW = P1A1dx1 – P2A2dx2
    dW = P1dV – P2dV = (P1 – P2)dV
    The work done on the fluid was due to conservation of gravitational force
    and change in kinetic energy. The change in kinetic energy of the fluid is given as:
    dK = 0.5m2v22−0.5m1v21=0.5ρdV(v22−v21)
    The change in potential energy is given as:
    dU = mgy2 – mgy1 = ρdVg(y2 – y1)
    Therefore, the energy equation is given as:
    dW = dK + dU
    (P1 – P2)dV = 0.5ρdV(v22−v21) + ρdVg(y2 – y1)
    (P1 – P2) = 0.5ρ(v22−v21) + ρg(y2 – y1)
    Rearranging the above equation, we get Bernoulli’s equation:
    P1+0.5ρv21+ρgy1=P2+0.5ρv22+ρgy2

    Fig.1 Experimental setup

    Processing of experimental results


    1. With the water meter coefficient a volumetric flow rate should be
    calculated:
    W =K × √ ∆ H ,
    2. With known dimensions for each cross section an average velocity should
    be calculated:
    V ave =W /S i,
    3. Velocity head:
    H v =V ave / g ,
    2

    4. For each cross section a specific energy should be evaluated:


    P
    H i= + H v,
    ρg
    5. Energy losses should be calculated for each cross section along the channel:
    ∑ hi=H i−H ,-
    Table 1.1 - Experimental and calculated data
    Cross section Si li zi+pi/ρg Vi ave V2i ave Hi Ʃhi
    /2g
    i cm cm cm cm/s cm cm cm
    1 6 0 17 0.15 150.15 4.66
    2 3.3 3.5 30.94 0.49 145.49 43.13
    3 1.5 8 68.1 2.36 102.36 6.74
    4 2.2 12.5 46.41 1.1 109.1 0.25
    5 3.9 17 26.18 0.35 109.35 0.83
    6 5.4 21.5 18.91 0.18 110.18 1.93
    7 6.9 26 14.8 0.11 112.11

    Conclusion:
    With Bernoulli´s equation we can describe the behavior of a fluid moving
    along a streamline, we can observe how the area of the pipe influenced the force
    and pressure of the liquid, the velocity and pressure will change their values
    according area of pipe and the density of the incompressible fluid remains
    constant at both points of the pipe.

    Group 230F Student Kevin Loachamin

    Final mark

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