Water flows through a horizontal tube of variable crosssection. The area of crosssection at A and B are 4 mm2 and 2 mm2 respectvely. If 1 cc of water enters per second through A, find (a) the speed of water at A, (b) the speed of water at B and (C) the pressure difference PA - PB

Given data:

Area of cross-section at A: 
           a1=4 mm2     = 4×10-6 m2

Area of cross-section at B: 
           a2=2 mm2     = 2×10-6 m2

Volume flow rate:
           Q=1 cc/s    =1×10-6 m3/s

Solution:

(a)

Volume flow rate, Q=a1v1

Speed of water at A:

       v1=QA1     =1×10-64×10-6      =0.25 m/s

(b)

Volume flow rate, Q=a2v2

Speed of water at B:

       v2=QA2     =1×10-62×10-6      =0.5 m/s

(c)

From Bernoulli's equation:

PAρ+vA22=PBρ+vB22PAρ-PBρ=vB22-vA22PA-PB=ρ2vB2-vA2               =100020.52-0.252                =93.8 Pa
 

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