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    Week 10: Non-Uniform Flow: University of Nueva Caceres College of Engineering and Architecture

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    Angelica Losares
    This document discusses non-uniform flow and hydraulic jumps. It begins with an introduction to hydraulic jumps, noting they occur during the transition from laminar to turbulent flow. The objectives are then stated as analyzing applications of hydraulic jumps. Several applications are listed, including water purification and irrigation. Formulas are provided for computing variables related to hydraulic jumps, such as the specific energy and minimum specific energy. Two example problems are worked through applying these formulas to rectangular channel problems involving hydraulic jumps.

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    Week 10: Non-Uniform Flow: University of Nueva Caceres College of Engineering and Architecture

    Uploaded by

    Angelica Losares
    111 views5 pages
    This document discusses non-uniform flow and hydraulic jumps. It begins with an introduction to hydraulic jumps, noting they occur during the transition from laminar to turbulent flow. The objectives are then stated as analyzing applications of hydraulic jumps. Several applications are listed, including water purification and irrigation. Formulas are provided for computing variables related to hydraulic jumps, such as the specific energy and minimum specific energy. Two example problems are worked through applying these formulas to rectangular channel problems involving hydraulic jumps.

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    This document discusses non-uniform flow and hydraulic jumps. It begins with an introduction to hydraulic jumps, noting they occur during the transition from laminar to turbulent flow. The objectives are then stated as analyzing applications of hydraulic jumps. Several applications are listed, including water purification and irrigation. Formulas are provided for computing variables related to hydraulic jumps, such as the specific energy and minimum specific energy. Two example problems are worked through applying these formulas to rectangular channel problems involving hydraulic jumps.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    111 views5 pages

    Week 10: Non-Uniform Flow: University of Nueva Caceres College of Engineering and Architecture

    Uploaded by

    Angelica Losares
    This document discusses non-uniform flow and hydraulic jumps. It begins with an introduction to hydraulic jumps, noting they occur during the transition from laminar to turbulent flow. The objectives are then stated as analyzing applications of hydraulic jumps. Several applications are listed, including water purification and irrigation. Formulas are provided for computing variables related to hydraulic jumps, such as the specific energy and minimum specific energy. Two example problems are worked through applying these formulas to rectangular channel problems involving hydraulic jumps.

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    © All Rights Reserved
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    University of Nueva Caceres

    College of Engineering and Architecture

    Week 10: Non-Uniform Flow

    I. Introduction
    A hydraulic jump is a fluid shockwave created at the transition between laminar and turbulent
    flow. One common example of a hydraulic jump can be seen in the water radiating outward
    when the stream of tap water strikes the horizontal surface of a sink. The water initially flows in
    a smooth sheet with consistent current patterns. In addition to the kitchen sink example,
    hydraulic jumps are also typical features of river rapids where the water swirls and foams
    around rocks and logs.

    In this chapter, you will learn different applications of hydraulic jump and how to solve problems
    related to it.

    II. Objectives
    After completion of the course the student should be able to:

    1. Analyze applications of Hydraulic Jump

    III. Hydraulic Jump


    Non- uniform flow occurs where the stream enters and leaves the channel at obstruction
    such as dams, weirs, bridges, or piers.

    The hydraulic jump is defined as the rise of water level, which takes place due to
    transformation of the unstable shooting flow (super-critical) to the stable streaming flow (sub-critical).
    When hydraulic jump occurs, a loss of energy due to eddy formation and turbulence flow occurs.

    Figure 15-1: Froude Numbers and Fluid Depths across a Hydraulic


    Jump

    HYDRAULICS V.1.0 BY:


    University of Nueva Caceres
    College of Engineering and Architecture

    Applications of Hydraulic Jump

     Usually, hydraulic jump reverses the flow of water. This phenomenon can be used to mix
    chemicals for water purification.
     Hydraulic jump usually maintains the high-water level on the downstream side. This high-water
    level can be used for irrigation purposes.
     Hydraulic jump can be used to remove the air from water supply and sewage lines to prevent
    the air locking.
     It prevents the scouring action on the downstream side of the dam structure.

    Figure 15-2: Flow Under a sluice gate accelerates from subcritical to


    critical to supercritical and then jump back to subcritical flow

    Formulas for Hydraulic Jump


    q2 ( d 1+ d 2 ) (d 1 d 2)
    =
    g 2
    Energy Head loss due to the jump
    3
    ( d 2−d 1 )
    HL =
    4 d1 d2
    (For rectangular channel unit)
    Height of Jump = d2 – d1
    Hydraulic Jump of Non-Rectangular Sections

    h1 A 1−h2 A 2
    Q2
    = 1 1
    g −
    A2 A1

    Where:

    HYDRAULICS V.1.0 BY: LOSARES 2


    University of Nueva Caceres
    College of Engineering and Architecture
    Q = rate of flow
    A1 = cross sectional area of section 1
    A2 = cross sectional area of section 2
    h1 = centroid of section 1 below the water surface

    h2 = centroid of section 1 below the water surface

    g = gravitational constant is 9.81 m/s2

    Example 1:

    A rectangular channel 2 m. wide carries 2.2 m 3/s of water in sub critical uniform flow at a depth of
    1.0 m
    a) Compute the specific energy
    b) Compute the minimum specific energy
    c) What is the lowest transverse hump in the bottom such that a critical depth is
    attained at the peak?
    Solution:
    a) Specific Energy b) Min. Specific Energy
    V2 2.2
    E= +d q=
    2g 2
    Q = AV q = 1.1 m3/s
    2.2 = 1 (2) V
    V = 1.1 m/s 2
    dc = 3 q
    E=
    V2
    2g
    +d √ g
    dc = 0.4978 m
    (1.1)2 3
    E= + 1.0 Emin = d
    2(9.81) 2 c
    E = 1.0617 m Emin = 0.7467 m

    c) Height of Jump
    h = E - Ec
    h= 1.0617- 0.7467
    h = 0.315 m

    Example 2:

    A vertical sluice gate with an opening of 0.67 m produces a downstream jet depth of 0.4
    m when installed in a long rectangular channel 5m wide conveying a steady discharge of 20
    m3/s. Assuming a hydraulic jump occurs and the flow downstream of the gate eventually returns
    to the uniform flow depth of 2.5 m.
    a) Compute the initial depth before hydraulic jump occurs.

    HYDRAULICS V.1.0 BY: LOSARES 3


    University of Nueva Caceres
    College of Engineering and Architecture
    b) Calculate the head loss in the jump

    HYDRAULICS V.1.0 BY: LOSARES 4


    University of Nueva Caceres
    College of Engineering and Architecture

    a) Initial depth before the jump occurs


    20
    q=
    5
    q = 4 m3/s/m
    q2 ( d 1+ d 2 ) (d 1 d 2)
    =
    g 2
    (4)2
    ( d + 2.5 ) (d 1∗2.5)
    = 1
    9.81 2
    d12 + 2.5d1 – 1.305 = 0
    d1 = 0.443 m

    b) Head loss at the jump


    V 21 V2
    + d1 = HL + 2 + d2
    2g 2g
    V1A1 = q
    V1(0.443)(1) =4
    V1 = 9.03 m/s

    V2A2 = q
    V2(2.5)(1) = 4
    V2 = 1.6 m/s
    ( 9.03 )2 (1.6 )2
    + 0.443= HL + + 2.5
    2(9.81) 2(9.81)
    HL = 1.97 m

    HYDRAULICS V.1.0 BY: LOSARES 5

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