Hydraulic Grade Lines

HYDRAULIC GRADE LINES
1. Graph the hydraulic grade lines as given five flow rates. Tell the detail of types of energy
variation and effect. Show the different type of sections of the system.
Hydraulic Grade line (HGL), it is a sum of the hydraulic energy point below the total energy point
at a different section. Here we have different type of 5 run, with the help there are manometer
value given in the table below:
Run 1 Run 2 Run 3 Run 4 Run 5
Measuring bucket
Volume (L) 1 1 1 1 1
Discharge Time (sec)
27.26 15.3 9.27 6.53 5.13
27.14 16.4 10.74 6.62 5.1
27.86 15.5 10.7 7.09 6.17
Manometer A
(mm) 156 168 193 235 261
Manometer B
(mm) 155 160 173 195 207
Manometer C
(mm) 151 151 153 154 152
Manometer D
(mm) 146 143 132 110 94
Manometer E
(mm) 141 128 101 48 13
Manometer F
(mm) 145 142 130 115 110
Value is available for the all Manometer phase as in the table, as per the table data graph plot
for the Hydraulic grade line.
Using formula
HGL= Z1 + 𝑃1/𝜌𝑔
Where z is the head datum, 𝑃/𝜌𝑔 head pressure

In this graph we study fives flow by run and having six manometer results. As per formula, while
entering the water inside the path, there is reduction in the manometer value at certain range point E.
where we have smallest section and next point where large area of section pressure increased suddenly.
Here are the losses such as a friction loss between pipe and water flow. [1]
Solution 2
First flow at the inlet velocity,
Let’s assume velocity on the inlet is V1, area A1,
Bernoulli’s equation
P1 + ρV12/2+ ρgz1= P2 + ρV22/2+ ρgz2
z1= z2
P1- P2 = ρ/2 (V22- V12)
As continuity equation
A1 V1= A2 V2
V2= A1 V1/ A2
Apply this in the above equation
P1- P2= ρ/2((A1 V1/ A2)2- V12)
V1= {2gh/ ((A1/ A2)2-1)}1/2
Where h is the pressure difference between A & B. 1

V1= {2*9.8*1/(( 25/ 13.9)4-1)}1/2
V1=1.44 m/s. Inlet Velocity
Similary for the throat velocity
V1= {2gh/(( A1/ A2)2-1)}1/2
Where h is 15
V1= {2*9.8*15/(( 10/ 25)4-1)}1/2
V1=17.41 m/s. throat Velocity
Similary for the outlet velocity
V1= {2gh/(( A1/ A2)2-1)}1/2
Where h is 4
V1= {2*9.8*4/(( 25/ 10)4-1)}1/2
V1=1.43 m/s. Outlet Velocity
For run 2
Inlet velocity 4.07m/s
Throat velocity 28.42m/s
Outlet velocity 2.68m/s
For run 3
Inlet velocity 6.43m/s
Throat velocity 43.11m/s
Outlet velocity 3.87m/s
For run 4
Inlet velocity 9.1m/s
Throat velocity 61.46m/s
Outlet velocity 5.87m/s