dd Air flows steadily from a tank through a hose of 0.03m diameter and exits to

Question

dd

Air flows steadily from a tank through a hose of 0.03m diameter and exits to the atmosphere from a nozzle of 0.01m diameter as shown in Fig. Q.4. The pressure in the tank (P1) remains constant at 3.0 kPa gauge and the atmospheric pressure and temperature arc 101 kPa and 15 degree C, respectively. Neglecting all losses as well as changes of the air density, determine: a) the velocity at exit ( V3). b) the flow rate and c) the pressure in the hose, i.e., P2. (ans.: a) 69.0 m/s; b) 5.42*10-3 m3/s, 6.83* 10-3 kg/s; c) 2.96 kPa gauge) Figure Q.4

Explanation / Answer

p1 = 3 kpa gauge => p1 = po + 3kpa

po = atmospheric pressure

p3 = 101 kpa = po

this is the pressure of the fluid just out of the nozzle.

we assume that the air has zero velocity in the large tank

consider it to be a tube of a very large diameter

then v1 = flow rate / a1 = 0

as a1 is very large

density of air = 1.27 kg/m3

this is standard result . u can get that by applying ideal gas eqution also.

put M = 28.9 g/mol

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