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# Tutor profile: Pratik B.

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Pratik B.
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## Questions

### Subject:Physics (Fluid Mechanics)

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Question:

There is a vertically symmetric glass with curvy walls and flat base, 10 cm in height. It can hold $$V$$ volume of a fluid. The base of the glass is octagonal in shape. Area of the base is $$A_b$$ and area of the top surface enclosed by a rim of the glass is $$A_t$$. The glass is filled fully with water. Find the net force applied by walls (excluding base) of the glass on the water for following cases: (a) Atmospheric pressure is zero (b) Atmospheric pressure is non Zero and equal to $$P_{atm}$$ (c) When will both the cases give the same answer?

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Pratik B.

This is a problem from fluid statics. There is always a way to calculate force applied by walls on water by using integration of small forces at each of the small elements of walls. But for that, we must know the profile of the walls. Here, we know very little about walls and have to calculate total (net) force by walls on water. So, we can try to find all forces on the water in the glass and equate their sum to zero as water is not accelerating. Forces on water inside glass are: 1. Gravity causes weight (Downward) ($$W$$) 2. Force by glass base (Upward) $$F_b$$ 3. Force by walls (Upward because walls of glass are vertically symmetric) $$F_w$$ 4. Atmospheric pressure at top (Downward) $$F_a$$ Net force in vertical should be zero. So, $$W+F_a=F_w+F_b$$ So, $$F_w=W+F_a -F_b$$ $$W=\rho \times V \times g$$ $$F=P \times Area$$, So, $$F_a= P_{atm} \times A_t$$ and for the base,, the magnitude of force applied by base on water is equal to the force applied by water on base. So, $$F_b= P_{base} \times A_b$$ Using simple statics equation, $$P_{base}=P_{top} + \rho \times g \times height$$. So, $$F_w= 1000 \times V \times 10 + P_{atm} \times A_t - (P_{atm}+ 1000 \times 10 \times 0.1) \times A_b$$ $$F_w= 10000V + P_{atm} (A_t-A_b) - 1000A_b$$ So this is the $$F_w$$ when $$P_{atm}$$ is not zero. When it is zero, the middle term disappears, and $$F_w$$ becomes, $$F_w= 10000V - 1000A_b$$ For (c), we want the middle term to go to zero all the time irrespective of the value of $$P_{atm}$$. So, $$0=P_{atm} (A_t-A_b)$$ $$A_t=A_b$$ This means that area of base and top should be same for the force to be independent of atmospheric pressure.

### Subject:Mechanical Engineering

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Question:

There is a container holding water at rest at STP. A small blade-fan is put into the water and operated for 1 min. The temperature of the water remains same throughout the process and there is no heat loss to the surrounding or to the fan. Explain the energy balance and KE of the water if the motor driving the fan is operated at 1 kW average. You may ignore the losses within the motor.

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Pratik B.

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