LECTURE 12: Water pressure, velocity & discharge measurements in...
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1 LECTURE 12: Water pressure, velocity & discharge measurements in pipes 12.1. Pitot Tube Energy Equation for point 1 & 2 z V + P z V + P h L z z At point 2 V 0 P P k.γ P k.γ∆h.γP P P γ.∆h V .P P = ...∆ = 2.g.∆h C V V V 2.g.∆h Dh k .1 .2 Patm Patm
Transcript of LECTURE 12: Water pressure, velocity & discharge measurements in...
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LECTURE 12: Water pressure, velocity &
discharge measurements in pipes
12.1. Pitot Tube
Energy Equation for point 1 & 2
z� � V���� +
P� � z� � V���� +
P� �hL
z� � z�
At point 2 V� � 0
P� � P��� � k. γ
P� � k. γ � ∆h. γ � P���
P� � P� � γ. ∆h
V� � ���.�P��P�� = ��.�..∆� = �2. g. ∆h
CV � V"#$%"&V$'()*($+#"&
,� � -.�2. g. ∆h
Dh
k
.1 .2
Patm
Patm
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12.2 Pitot tube in conjuction with a static tube
P/01�2�3/4H2�6 � P �z
P/201�2�3/4 P3288932 � P+γz
z� � V���� +
P� � z� � V���� +
P�
V� � 0
V� � �2. g. ∆ :P � z;
P� � γ. �z� � z<� � γ�. �z< � z=� � P= � P>
P� � γ. �z� � z?� � γ. �z? � z>�
z? � z<
z? � z> � z< � z=
�P� � γ. z�� � γ�. ∆h � �P� � γ. z�� � γ. ∆h
�P� � γ. z�� � �P� � γ. z�� � �γ� � γ�. ∆h
@P�γ � z�A � @P�γ � z�A � @γ� � γγ A . ∆h
V� � Cv �:���CD�∆� ;
Difference in pressure
and elevation heads
1
2
3
4
6
5
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12.3. Venturimeters
Q � A���A�/A����� . �2. gH�P� � P��/γ � z� � z�I
Cd=Discharge Coefficient
Q � A�. C6. �2. g. K∆�P/γ� � zL Q � A�. C6. �2. g. ∆�P/γ�
12.4 Nozzle Meter and Orifice meter
The coefficient of disccharge for nozzle meters and orifice meters can not be computed
directly from the area ratio, A1/A2. The discharge equations must be modified by an
experimental, dimensionless coefficient, Cv.
Q � A�. CMC6. N2g. O∆ @Pγ � zAP
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(a) Nozzle meter and (b) orifice meter
Example 12.1. A 6 cm(throat) Venturi meter is installed in a 12 cm diameter horizontal water
pipe. A Differential (mercury-water) manometer is installed between the throat and the entry
section registers a mercury (sp. Gr =13.6) column reading of 15.2 cm. Calculate the dicharge.
∆P � ∆h. HγH� � γI
∆P � ∆h. :HR� ;
� ∆h. K13.6 � 1L
∆P � �15.2 cm�. �12.6�
A� � Y.D�> �
Y.���> � 113 cm�
A� � Y.D�> �
Y.<�> � 28.3 cm�
C6 � ���A�/A����� � 0.259
Q � �0.259�. �113/10000�. �2. �9.81�. �15.2/100�. �12.6�
Q=0.0179 m3/s
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Example 12.2: The Venturi meter in Example 12.1 is replaced with an ASME flow nozzle
meter. During operation, the attached differential (mercury – water) manometer registers a
mercury column reading of 15.2 cm. The water in the pipeline is 20]. Determine the
discharge.
C6 � 0.259
We assume it
Assume experimental meter coefficient CV as 0.99
Q � �0.99�. �0.259�. �113/10000�. �2. �9.81�. �15.2/100�. �12.6�
Q � 0.0178 m?/sec
Check Reynolds number of the nozzle.
NR � V�.6�c �
d�e.e�fg�/:�Y/>�.�</�ee��;h.�e.e<��.eei�eDj
� 3.78 i 10=
From Figure 9.8 , Cv=0.986
Corrected discharge: Q � �0.986�. �0.259�. 0.0178=0.0177 m3/s
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