The mass of air displaced will be double for the same speed. The back pressure of air will be double. Therefore, four times.
Sasha, Are you up to you tricks again? Lets assume the airflow is incompressible. Let power of the vacuum be equal to the kinetic energy added to air over a certain time t P=[ .5 m v^2]/t m=Vp m - mass of air v- velocity of air (related to the RPM of the motor) p - density of air So what is P1/P2? P2 - normal density of air and P1 is twice the normal density. We have P1/P2=[ .5 m1 v1^2]/t1 / [ .5 m2 v2^2]/t2 since t1=t 2 and v1=v2 P1/P2=m1/m2 P1/P2=V1p1/V2p2 since V1=V2 P1/P2=p1/p2=2 So the power will be doubled for doubling the density... ********** But wait! ********** If vacuum cleaner works by creating an air flow and it is air molecules that whip the dust particles out of their hiding places then we may drop the rpm of the motor by half and therefore the power will be the same. P1=P2
