Question

In a pipe flow, the hydraulic grade line will be obtained by the summation of

• A. Pressure head and datum head
• B. Velocity head and datum head
• C. Pressure head and velocity head
• D. Pressure head, velocity head and datum head

Hint:

A simple way to remember the energy lines:
- HGL = Piezometric Head ($z + P/\gamma$)
- EGL = Total Head (HGL + Velocity Head)
The vertical distance between the EGL and HGL is always the velocity head, $v^2/2g$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the definition of the Hydraulic Grade Line (HGL) in pipe flow.

Step 2: Detailed Explanation:
In pipe flow analysis using the Bernoulli equation, we often work with three types of "head":
-

Datum Head ($z$): The potential energy per unit weight, representing the elevation of the point above a reference datum.
-

Pressure Head ($P/\gamma$): The flow work energy per unit weight.
-

Velocity Head ($v^2/2g$): The kinetic energy per unit weight.
Two important energy lines are defined:
1.

Total Energy Line (TEL) or Energy Grade Line (EGL): This line represents the total head (total energy per unit weight) of the fluid along the pipe.
\[ EGL = z + \frac{P}{\gamma} + \frac{v^2}{2g} \] In real flow, the EGL always slopes downwards in the direction of flow due to head loss from friction.
2.

Hydraulic Grade Line (HGL): This line represents the piezometric head. It is obtained by the summation of the

pressure head and the datum head.
\[ HGL = z + \frac{P}{\gamma} \] The HGL is always located below the EGL by a vertical distance equal to the velocity head ($v^2/2g$). The HGL represents the level to which liquid would rise in a piezometer tube attached to the pipe.

Step 3: Final Answer:
The hydraulic grade line is obtained by the summation of the pressure head and datum head.