HP 48gII Graphing, 50g Graphing manual 456

Equations:

	----P--		+ v----2----2---–----v----1---2-						+ g ⋅ y = 0
	ρ					2
			2 ⋅ 			 A2 2
----P--	v2				1 – 		A-----1--		 
	+ ------								------+ g ⋅		y = 0
				-------------				---2--------------
ρ
	v1	2		⋅		A2		2	
						A-----1-		– 1
----P--									
	+ --------------------					--2-----------------			------ + g ⋅		y = 0
ρ
P = P2 – P1					y = y2 – y1						M = ρ ⋅ Q
Q = A2 – v2									Q = A1 – v1
	π ⋅		D12						A2 =	π ⋅ D22
A1 = -----------------										------	--4---------
			4

Example:

Given: P2=25_psi, P1=75_psi, y2=35_ft, y1=0_fr, D1=18_in, ρ=64_lb/ft^3, v1=100_ft/s.

Solution: Q=10602.8752_ft^3/min, M=678584.0132_lb/min, v2=122.4213_ft/s, A2=207.8633_in^2, D2=16.2684_in, A1=254.4690_in^2, ΔP= -50_psi, Δy=35_ft.

Flow with Losses (3, 3)

These equations extend Bernoulli’s equation to include power input (or output) and head loss.

Equations:

M ⋅

 ----P-- + v----2---2----–----v----1---2-

+ g ⋅

y + hL = W

 ρ

2





v2

2

⋅



 A2 2





----P--

1 – 

A-----1--

 



M ⋅ 

+ -------

+ g ⋅ y + hL = W

-------------------------------------



ρ

2









v1

2

⋅



A1 2









A-----2--

– 1



----P--

+ -------



+ g ⋅

M ⋅ 

-------------------------------------

y + hL = W



ρ

2







P = P2 – P1

y = y2 – y1

M = ρ ⋅ Q

Q = A2 ⋅ v2

Q = A1 ⋅ v1

π ⋅

D12

A2 =

π ⋅ D22

A1 = -----------------

--------4---------

4

5-20 Equation Reference