FEexam review 47: Fluid Mechanics 7 – Orifice Velocity Explained

Описание: Can You Solve This? FE Fluid Mechanics – Orifice Discharge Velocity

In this video we solve a classic FE Civil Fluid Mechanics problem: four water tanks with different heads discharge through small orifices freely into the atmosphere. Which tank has the fastest jet? We use Torricelli’s theorem and the orifice discharge equation exactly as shown in the NCEES FE Reference Handbook.

Concept Overview
When water exits a sharp-edged orifice to the atmosphere, the jet speed depends on the head h. With losses captured by the discharge coefficient C, the velocity is V = C*sqrt(2*g*h). Since C is the same for all tanks, the higher the head, the higher the velocity.

00:00 – Introduction to Orifice Velocity Problem
00:29 – Understanding the Discharge Velocity Formula (V = C × √(2gH))
01:11 – Calculating Velocity for Tank A
01:52 – Calculating Velocity for Tank B
02:15 – Calculating Velocity for Tank C
02:34 – Calculating Velocity for Tank D
02:55 – Matching Velocities to Tanks
04:02 – Relationship Between Water Head and Discharge Velocity


Key Formulas (NCEES FE Reference Handbook, page 107)
Orifice discharge (flow rate):
Q = C* A* sqrt(2*g*h)

Velocity of discharge (derived from Q/A_o):
V = C * sqrt(2*g*h)

Symbols:
Q = discharge, ft^3/s
V = velocity, ft/s
C_d = coefficient of discharge (use 0.6 in this problem)
A_o = orifice area, ft^2
g = 32.2 ft/s^2
h = head above the orifice center, ft

Step-by-Step Solution
1) Write V = C*sqrt(2*g*h).
2) Substitute C = 0.6, g = 32.2 ft/s^2, and the given h for each tank.
3) Compute V for each tank.
4) Compare. Larger h gives larger V.


NCEES FE Reference
Section: Fluid Mechanics – Flow through orifices and nozzles
Page: 107 (use Q = C_d * A_o * sqrt(2*g*h) and derive V)

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