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# two -dimensional fluid flow

الكلية كلية الهندسة     القسم  الهندسة المدنية     المرحلة 3
أستاذ المادة يحيى كاظم حسين التميمي       20/03/2017 06:56:33
Two dimensional fluid flow constructed as
a- Flow of water take place from point of high head to point of low head
b- The flow is generally laminar.
c- The path taken by a water molecules is represented by a flow line.
d- Although an infinite number of flow lines can be drawn for convenience only a few are drawn.
e- At certain points on different flow lines, the total head will be the same
f- The lines connecting points of equal total head can be drawn. These lines are known as equipotential lines.
g- The flow always take place a long steepest hydraulic gradient.
h- The equipotential lines cross flow lines at right angles, and these lines together from a flow net.
i- The flow net gives a pictorial representation of the path taken by water molecules and the pressure variation a long that path.
*flow net for one dimensional flow
The figure below shows a tube ( 1.2 *1.2m) in cross-section by 4.8m high through which steady- state vertical flow is occurring .
Q = kiA = 0.05 *10-2 m/sec * (4.8/3) *1.2*1.2 = 0.00115 m3/s
If a dye placed on the top of the soil ( elevation 3.6) the movement of the dye through the soil give vertical flow line ( flow path or stream line )
• For convenience , five flow lines are shown on one channel in to another
• From the flow net the soil engineer can determine three vary useful items of information : rate of flow ; heads and gradient
1- The rate of flow through the soil : - consider square A
qA= kiA.aA
iA = ???????? where
H = total head lost in flow
l = vertical dimension of A
aA = cross – sectional area = b*L where L = the dimension perpendicular to the page = 0.3 m
qA= ?????????????? ; b=l ( the shapes are square ) and L = 1 unit
qA= ????????
the flow per unit length L perpendicular to the page
????=???? ???? = ????????????
= ???????????? = kH§
§= ????????=410=0.4
???? = kH§ = 0.005*10-2 * 4.8 * 0.4 = 0.0096 m3/sec.
??=?????1.2= 0.0096*1.2 = 0.00115 m3/sec.
2- Determination of head at any point:-