HP 48gII Graphing, 50g Graphing manual Forces and Energy, Flow in Full Pipes 3

Example:

Given: P2=30_psi, P1=65_psi, y2=100_ft, y1=0_ft, ρ=64_lb/ft^3, D1=24_in, hL=2.0_ft^2/s^2, W=25_hp, v1=100_ft / s.

Solution: Q=18849.5559_ft^3/min, M=1206371.5790_lb/min, P =35_psi, y =100_ft, v2=93.1269_ft /s, A1=452.3893_in^2, A2=485.7773_in^2, D2=24.8699_in.

Flow in Full Pipes (3, 4)

These equations adapt Bernoulli’s equation for flow in a round, full pipe, including power input (or output) and frictional losses. (See “FANNING” in Chapter 3.)

Equations:

ρ

⋅



π ⋅ D2

⋅ vavg ⋅

 ΔP

+ g ⋅ Δy + vavg

2

⋅



2

⋅ f ⋅

 L 

+

ΣK

= W



4 

 ρ



 D

2 

ΔP = P2 – P1

Δy = y 2 – y 1

M = ρ ⋅ Q

π ⋅ D

2

D ⋅ vavg ⋅

ρ

n = ∝

Q = A ⋅ vavg

A =

Re =

4

∝

ρ

Example:

Given: ρ=62.4_lb/ft^3, D=12_in, vavg= 8_ft/s, P2=15_psi, P1=20_psi, y2=40_ft, y1=0_ft, ∝=0.00002_lbf∗s/ft^2, ΣK=2.25, ∈=0.02_in, L=250_ft.

Solution: P =5_psi, y =40_ft, A=113.0973_in^2, n=1.0312_ft^2/s, Q=376.9911_ft^3/min, M=23524.2358_lb/min, W=25.8897_hp, Re=775780.5.

Forces and Energy (4)

VARIABLE	Description
α	Angular acceleration
ω	Angular acceleration
ωi,ωf	Initial and final angular velocities
ρ	Fluid density
τ	Torque
Θ	Angular displacement
α	Acceleration

Equation Reference 521