An air tank of volume 1.5 m3 is initially at 800 kPa and 208C. At t 5 0, it begins exhausting through a converging nozzle to sea-level conditions. The throat area is 0.75 cm2 . Estimate (a) the initial mass fl ow in kg/s, (b) the time required to blow down to 500 kPa, and (c) the time at which the nozzle ceases being choked.

(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

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)