(5) Gas flow equation
dM i
dt
¼ G i
ð11:35Þ
where
M i Gas mass in front and rear chamber;
G i Gas mass per unit time.
When calculating the gas flow rate inflow or exhaust the front and rear chamber,
it is necessary to first calculate the wind speed through the throttle, determine what
kind of sound speed it belongs to, and then select the corresponding calculation
equation. The intake and exhaust process of the chamber is adiabatic expansion
process, and the type of sound velocity can be determined by the critical pressure
ratio e:
e ¼
2
k þ 1
k
k þ 1
ð11:36Þ
When p 2 =p 1 ¼ e, the velocity of gas flow is equal to the speed of sound; when
1 ! p 2 =p 1 ! e, the velocity of gas flow is less than the first velocity, i.e., subsonic
velocity; when 0 p 2 =p 1 e, it is calculated as supersonic velocity.
Equation for calculating when subsonic velocity
G ¼ CS
p 1
ffiffiffiffiffiffi
RT
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2k
k À 1
p 2
p 1
2
k À
p 2
p 1
k þ 1
k
"
#
v
u
u
t
ð11:37Þ
Equation for calculating when supersonic velocity
G ¼ CS
p 1
ffiffiffiffiffiffi
RT
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2k
k þ 1
2
k þ 1
2
kÀ1
s
ð11:38Þ
where
k
Adiabatic process index;
S
Section area of intake and exhaust port;
p 1 ; p 2 Pressure at inlet and outlet of air chamber;
T
Thermodynamic temperature of gas in front and rear chambers.
230
11 Pneumatic Down-the-Hole Hammer