A water pipe abruptly narrows at a constriction, causing velocity to increase significantly. Immediately downstream of the constriction, how do the energy grade line (EGL) and hydraulic grade line (HGL) behave compared to upstream?
ABoth the EGL and HGL rise because the higher velocity increases total energy
BThe EGL drops only slightly (minor losses) while the HGL drops sharply because velocity head increases and pressure head falls
CBoth EGL and HGL drop by the same amount because energy is conserved through the constriction
DThe HGL rises at the constriction because higher velocity means higher dynamic pressure
At a constriction, velocity increases so V²/2g (velocity head) increases. Since EGL = HGL + V²/2g, and EGL drops only slightly (minor loss from the constriction), the HGL must drop sharply to make room for the larger velocity head. This is exactly what a Venturi meter exploits: the HGL drop at the throat measures the velocity increase. Option D is a common confusion — static pressure actually falls at high-velocity sections (Bernoulli principle).
Question 2 Multiple Choice
The hydraulic grade line (HGL) dips below the physical centerline of a pipe at a particular location. What does this indicate about conditions at that point?
AThe flow velocity has dropped below a minimum threshold required to maintain turbulent flow
BThe gauge pressure at that location is negative, meaning absolute pressure is below atmospheric, creating a risk of cavitation or flow separation
CThe pipe must slope upward at that location, creating an adverse pressure gradient
DThe energy grade line has also dropped below the pipe centerline, indicating total energy loss
The HGL represents z + P/(ρg) — the sum of elevation and pressure head. When the HGL drops below the pipe centerline, P/(ρg) is negative at that elevation, meaning gauge pressure is below atmospheric. Physically, the fluid is being 'pulled' into tension. If the pressure drops to the vapor pressure of the liquid, cavitation occurs — vapor bubbles form and collapse violently, causing noise, erosion, and loss of pumping capacity. This is why engineers check HGL position when designing pipe systems at high elevations.
Question 3 True / False
The hydraulic grade line (HGL) and energy grade line (EGL) are generally parallel to each other along a pipe because both represent forms of energy conservation.
TTrue
FFalse
Answer: False
The EGL and HGL differ by exactly the velocity head V²/(2g). They are parallel only when velocity is constant along the pipe (constant cross-section). Wherever the pipe changes diameter, velocity changes, so the gap between EGL and HGL changes — they diverge or converge. At a constriction (higher velocity), the HGL drops closer to the EGL; at an expansion (lower velocity), the HGL rises toward the EGL. Thinking they are always parallel leads to errors in pressure prediction.
Question 4 True / False
In a frictionless flow with no pumps or turbines, the energy grade line is horizontal along the entire pipe, meaning total head is the same at every cross-section.
TTrue
FFalse
Answer: True
Total head H = z + P/(ρg) + V²/(2g) is conserved in frictionless flow — this is just Bernoulli's equation rewritten in head form. A horizontal EGL means energy is neither added nor lost: conversion between elevation, pressure, and velocity head occurs freely, but the total remains constant. In real flows, friction and local losses cause the EGL to slope downward in the direction of flow. Pumps create an upward jump; turbines create a downward drop.
Question 5 Short Answer
Explain what the energy grade line (EGL) represents physically and why it always slopes downward in the direction of flow in a real pipe system.
Think about your answer, then reveal below.
Model answer: The EGL represents the total mechanical energy per unit weight of fluid at each cross-section, expressed as a height: H = z + P/(ρg) + V²/(2g). It slopes downward in the direction of flow because real flows lose mechanical energy to heat through viscous friction in the pipe walls and local losses at fittings, valves, and changes in geometry. This lost energy cannot be recovered — it is irreversibly converted to thermal energy. The slope of the EGL (head loss per unit length) is called the hydraulic gradient and directly quantifies how much energy is being consumed by friction.
The downward slope of the EGL is the visual signature of head loss. A steeper slope means faster energy dissipation — long pipes, rough surfaces, or high velocities. If the EGL were horizontal, friction would be zero (ideal fluid). The practical value of sketching the EGL is that it immediately shows where energy is going in a pipe network, where pumps must add head, and whether the available head is sufficient to push flow to its destination.