Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vit), can be expressed as: Reservoir v(t) V2gh tanh 2L 2gh) water Pipe Where h is the helght of the fluid in the reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vit) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh tanh (유V2gh) water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xun = 0.1, xg = 1, e = 0.001 and If (Xnew)l < E
Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vit), can be expressed as: Reservoir v(t) V2gh tanh 2L 2gh) water Pipe Where h is the helght of the fluid in the reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vit) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh tanh (유V2gh) water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xun = 0.1, xg = 1, e = 0.001 and If (Xnew)l < E
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Transient Orifice Flow:
Water is discharged from a reservoir through a long pipe as shown. By
neglecting the change in the level of the reservoir, the transient velocity of
the water flowing from the pipe, vt), can be expressed as:
- Reservoir
v(t)
V2gh
= tanh V2gh)
Pipe
Where h is the height of the fluid in the
7-
reservoir, L is the length of the pipe, g is the
acceleration due to gravity, and t is the time
elapsed from the beginning of the flow
Transient Orifice Flow:
Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds,
given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to
gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters.
Reservoir
v(t)
V2gh
= tanh
2L
2gh
water
Pipe
Hint: Transform the equation to a
function of form: fih) = 0
Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS,
starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < E
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