# E16 Gas

HBD Gas Status, trend
CALC
Remaining CF4 CALC

## 直管の圧力損失

$\Delta p = \lambda \frac{l}{d} \cdot \frac{1}{2}\rho V^2$

• $\lambda$:管摩擦係数
• $l$:管の長さ
• $d$:管の直径
• $\frac{1}{2}\rho V^2$: 動圧[Pa]

#### 管の長さ

• 3/8" 1000mm → l/d = 133.
• 1/4" 1000mm → l/d = 230.

#### 管摩擦係数 $\lambda$

##### Re < 2300 （層流）

$\lambda = \frac{64}{Re}$

##### 乱流

BA管は粗さk<3$\mu$mであり、1/4inchでも$Re=10^5$くらいまではなめらかとみなせる。
なめらかでない場合はニクラゼの実験値を使う。

$\lambda = 0.3164 Re{}^{-0.25} (3 \times 10^3 < Re < 10^5)$

$\lambda = 0.0032 + 0.221Re^{-0.237} (10^5 < Re < 3 \times 10^6)$

#### Example

mHBD Gas flow: 1/4 air 1L/min 20m pipe :
• Re=348, $\lambda=0.18$
• Dyn. press. = 0.815
• Pressure Drop = 0.18 * 230 * 0.815 * 20 = 674 Pa.
well below 100kPa (atomosphere).

### 動圧 Dynamic Pressure

P = $\frac{1}{2}\rho v^2$
[kg/m${}^3$ $\times$ (m/s)${}^2$ = kg m/s${}^2$ $\times$ 1/m${}^2$ = N/m${}^2$ = Pa]

### Reynolds Number

$Re = \frac{Vd}{\nu}$
[m/s m /(m2/s)] = []

Pipe Gas flow [L/min] Dyn. Pressure[Pa] Re
1/4" Air 1.0 0.815 348
1/4" Air 2.0 3.26 696
1/4" CF4 1.0 2.29 1059
1/4" CF4 2.0 9.16 2118
3/8" Air 1.0 0.0914 199
3/8" CF4 1.0 0.257 614
3/8" CF4 4.0 4.11 2455

### Pipe standards / velocity

Pipe Out. Dia.[mm] In. Dia.[mm] X sec.[mm${}^2$] v[m/sec]
at 1L/min
1/4" 6.35 4.35 14.9 1.12
3/8" 9.53 7.53 44.5 0.375
1/2" 12.7 10.7 89.9 0.185
NW25($\sim$1") 27.2 23 416 0.0400

### Viscosity

Gas $\mu$ [mPa$\cdot$s] $\rho$ [kg/m${}^3$] $\nu$[m${}^2$/s]
Air 0.0181 1.3 1.4 $\times 10^{-5}$
Ar 0.0222 1.8 1.2 $\times 10^{-5}$
CF4 unknown (0.02) 3.65 0.55 $\times 10^{-5}$
CF4 0.0167(at 15degC) 3.65 0.46 $\times 10^{-5}$

#### A note on the viscosity of CF4

Temp[K] uPa s
275K 16.06
300K 17.31
16.7 at 15 degC.
J.J. Hurly et al.

### Bubbler

Silicone oil: KF-96-50cs

$\rho=$ 960 [kg/m3]
Bubler height 1mm = 9.4 Pa