Hydraulics Lab - ECIV 3122
Experiment (5): Flow through small orifices
Exp. (5): Flow through small orifices
Purpose:
To study the flow through small orifice discharging to atmosphere and determine the
discharge coefficient, velocity coefficient and the actual jet profile.
Apparatus: Small Orifices Apparatus (Fig. 1).
Figure (1): Small orifices apparatus
Theory:
Figure(2) : Vena Contracta
The stream line of the orifice contract reducing the area of flow (Vena Contraction).
𝐴𝑎𝑐𝑡𝑢𝑎𝑙 = 𝐶𝑐 . 𝐴
Where: Cc is the coefficient of contraction.
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Hydraulics Lab - ECIV 3122
Experiment (5): Flow through small orifices
Figure (3) : Apply Bernoulli eqn
For water at a level of H above the orifice, apply Bernoulli’s equation from the top
surface to the orifice:
𝑇𝐻𝐴 = 𝑇𝐻𝐵 + 𝐻𝐿 𝐴→𝐵
Then the velocity of water discharge through the orifice can be written as:
𝑉𝐵(𝑇ℎ.) = √2𝑔𝐻
Where:
-
Head losses assumed to be zero.
-
g is acceleration due to gravity (m/s2)
-
H is the water height (m)
Figure (4) : Trajectory Motion
The jet velocity trajectory consists of two components. At the exit of the orifice the
vertical component is zero, thus the velocity leaves the orifice horizontally. Neglecting
air resistance, the horizontal velocity can be considered as a constant and equal to V.
Apply the law of constant velocity motion in x-direction and third law of constant
acceleration motion (g) in y-direction:
𝑥
𝑡=
𝑣
1
𝑦 = 𝑣°𝑦 𝑡 + 𝑔𝑡 2
2
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Hydraulics Lab - ECIV 3122
Experiment (5): Flow through small orifices
Then the velocity of water discharge through the orifice can be written as:
𝑔
𝑣𝑎𝑐𝑡. = 𝑥 . √
2𝑦
𝐶𝜈 =
𝑣𝑎𝑐𝑡
𝑥
=
… … … … … … … … … . . 𝑒𝑞𝑛 (1)
𝑣𝑡ℎ
2√𝐻 √𝑦
So, there are two reasons for the difference between theoretical and actual discharge:
𝐶𝑑 =
𝑄𝑎𝑐𝑡.
𝑉 ⁄𝑡
=
𝑄𝑇ℎ.
𝐴√2𝑔𝐻
… … … … … … … . … 𝑒𝑞𝑛 (2)
The range of Cd values (0.60-0.65)
𝐶𝑑 = 𝐶𝑣 × 𝐶𝑐 … … … … … … … … … … … … . 𝑒𝑞𝑛 (3)
Procedure:
1. Fix 8 mm diameter orifice in the side of the tank.
2. Switch the pump on; allow water to rise until reaching a height of 25 cm.
3. Measure the flow rate (volume collected in certain time) .
4. Measure the trajectory of jet using Hook Gauge.
5. Record the value of x and the corresponding y value.
6. Control the flow valve to increase water height to 50 cm, then repeat the previous
steps.
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Hydraulics Lab - ECIV 3122
Experiment (5): Flow through small orifices
Data & Results:
1. Draw a relationship between Qact. in y-axis & √𝐻 in x-axis. Determine the slope
of the graph, then calculate Cd ( eqn.2).
𝐶𝑑 =
𝑠𝑙𝑜𝑝𝑒
𝐴√2𝑔
2. Draw the trajectory of jet for H=50cm (x & -y values).
3. Plot graphs of 𝑥 against √𝑦 (x in y-axis & √𝑦 in x-axis) for H=50cm.
Determine the slope of the graph, then calculate Cv (eqn.1).
𝐶𝑣 =
4.
𝑠𝑙𝑜𝑝𝑒
2√𝐻
Calculate the coefficient of contraction (eqn.3).
H (cm)
50
25
Qth (m3/s)
V (L)
t (sec)
Qact (m3/s)
√𝐻 (m)
H=50cm
x (cm)
0
10
15
20
25
y (mm)
x (m)
y (m)
√𝑦(𝑚)
4
30
35
40
45
50