Answer:
(a) m = 0.141 kg/s
(b) t = 47.343 s
(c) t = 143.745 s
Explanation:
Given that:
The volume of air in the tank V = 1.5 m³
The initial temperature in the tank is supposed to be 20° C and not 208 C;
So
The initial pressure in the tank
The throat area = 0.75 cm²
To find the initial mass flow in kg/s.
Lets first recall that:
Provided that , then the flow is choked.
Then;
From what we see above, it is obvious that the ratio is lesser than 0.528, therefore, the flow is choked.
Now, for a choked nozzle, the initial mass flow rate is determined by using the formula:
where;
where;
T = 244.16 K
During a critical condition when Mach No. is equal to one;
V = 313.214 m/s
Thus, the initial mass flow rate
m = 6.03 × 0.75 × 10⁻⁴ × 313.214
m = 0.141 kg/s
(b)
The mass balance formula for the control volume surrounding the tank can be expressed as:
When the air mass flow rate is:
Thus; replacing in the previous equation; we have:
Taking the differential of both sides from 0 → t
So, when the pressure P = 500 kPa, the time required is:
t = 47.343 s
(c)
Let us recall that:
The choking on the nozzle occurred when
From ; the time required for is:
By solving:
t = 143.745 s