Statement I: For idealized Bernoulli's flow through a pipe, the E
Statement I: For idealized Bernoulli's flow through a pipe, the Energy grade line is always horizontal and Hydraulic gradient line is parallel to the Energy grade line.
Statement II: Hydraulic gradient line is defined as the line which gives the sum of pressure head (p/γ) and datum head (z) of a flowing fluid in a pipe w.r.t some reference line.
A. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
B. Both Statement (I) and Statement (II) are individually true but Statement (II) is <span style="font-weight: 700;">not</span> the correct explanation of Statement (I)
C. Statement (I) is true but Statement (II) is false
D. Statement (I) is false but Statement (II) is true
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Concept:
Energy gradient line is defined as the line which gives the sum of pressure head, datum head, and kinetic head of a flowing fluid in a pipe with respect to some reference line.
\(TEL = \frac {p}{γ}+\frac {V^2}{2g}+z\)
Pressure head - p/γ
Kinetic head - V2/2g
Datum head - z
For idealized Bernoulli flow, losses are zero and TEL will be nothing but the Bernoulli equation which is always constant. Hence, it will be horizontal.
Hydraulic gradient line is defined as the line which gives the sum of pressure head (p/γ) and datum head (z) of a flowing fluid in a pipe w.r.t some reference line.
\(HGL = \frac {p}{\gamma}+z\)
For HGL to be constant (Horizontal), the velocity should be constant (uniform). Here, it is not mentioned uniform diameter, so it is not always horizontal.
Therefore, statement I is false and statement II is true.