Question

Suppose the tube in the previous problem is kept vertical with B upward. Water enters through B at the rate of 1 cm3 s−1. Repeat parts (a), (b) and (c). Note that the speed decreases as the water falls down.

Answer 1

(a) The speed at A,  =25 cm/s

(b) The speed at B,  =50 cm/s

(c) The Bernoulli theorem  =187.5 N/m² ≈ 188 N/m²

Explanation:

Because the discharge through the tube remains the same i.e. 1 cm3/s, the speeds at A and B are the same.

(a) The speed at A,

v =1/0.04 cm/s =100/4  cm/s =25 cm/s    

(b) The speed at B,  

v' =1/0.02  cm/s =100/2  cm/s =50 cm/s  

(c) Because the end B is upward, we take end A as the height reference point. So end height A = 0 and end height B = h  =15/16 cm  =15/1600 m.  

The Bernoulli theorem

Pₐ+1/2 ρv² = Pᵦ+1/2 ρv'²+ρgh  

Pₐ-Pᵦ =1/2 ρ(v'²-v²) +ρgh  

=1/2×1000×(0.50²-0.25²) +1000×10×15/1600  N/m²  

=1/2×1000×0.75×0.25 +  1500/16  N/m²    

=93.75 + 93.75 N/m²  

=187.5 N/m² ≈ 188 N/m²

Answer 2

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