A fan is to be selected to ventilate a bathroom whose...

A fan is to be selected to ventilate a bathroom whose dimensions are 2.5 m x 3m x 3 m. The air velocity is not to exceed 7 m/s to minimize vibration and noise. The combined efficiency of the fan-motor unit to be used can be taken to be 60 percent. If the fan is to replace the entire volume of air in 10 min, determine the power of the fan-motor unit. Take the air density to be 1.25 kg/m³ and disregard the effect of the kinetic energy correction factors. Select one: a. 2.914 W b. 19.14 W c. 1.914 kW d. 1.914 W

Transcript

00:02 Hi, for this problem, we are told to find the rating of a fan motor unit to want to buy and to also find the size of the fan and what the pressure difference across the fan will be.

00:16 Now, the electrical rating of a fine, i'll call it this, is simply equal to the effective fan power divided by the efficiency of the fan and motor connection.

00:39 Now, we were giving this efficiency as 50%.

00:44 So to find this electrical rating, all we need to do is to find the effective fan power.

00:54 Now, from the energy equation, i can simply write that the mass flow times this plus the kinetic energy correction factor times v1 square over 2 plus gz1 plus the effective fan power output is going to be equal to the same mass flow p2 over row plus alpha 2 v2 square over 2 plus gz2 now, if i model this fan this way, let this be my fan, and i put station one here and station two here.

01:58 You can see that at these very far locations, very far from the fan, i can simply write that p1 at this point is simply atmospheric pressure, also very far away from the fan.

02:11 P2 is also atmospheric pressure.

02:15 This is the inlet to the fan, this is the outlet.

02:20 Also, z1 here will be equal to z2.

02:24 The levels are the same both at the inlet and the outlet.

02:30 We see also that at this inlet position quite far away from the fan, we can see that v1 there is equal to zero.

02:40 Now, the problem also asked us to neglect the kinetic energy correction factors.

02:46 So i can just say that alpha 1 is 1 and alpha 2 is 1.

02:50 And if i apply all this, my equation becomes the effective work output of the fan is simply going to be equal to the mass flow rate times v2 squared over 2.

03:12 Now, what is the mass flow rate across the fan? it's simply the density of air times this.

03:22 But we know also that area times velocity is the same thing as what the flow rate, the voice, the volume.

03:28 Volume flow rates.

03:31 Now we are told that this fan changes the entire volume of air in the bathroom every 10 minutes.

03:40 What it means is that the mass flow rates would then be equal to the density of air times the volume of the bathroom changed every 10 minutes...

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