Question

Water flows through a tube shown in figure (13-E8). The areas of the cross-section at A and B are 1 cm² and 0.5 cm² respectively. The height difference between A and B is 5 cm. If the speed of the water at A is 10 cm/s find (a) the speed at B and (b) the difference in pressure at A and B.

Answer 1

Figure of this question is attached in an solution provided below.

Now, By the equation of the continuity, Area is inversely proportional to the velocity. Also, The Product of area and velocity is constant for an given horizontal pipe.

(a). A₁V₁ = A₂V₂

1 × 10 = 0.5 × V₂

V₂ = 20 cm/sec.

Hence, the velocity of the fluid at B is 20 cm/sec.

(b). Using the Bernoulli's Theorem,

  P₁ + h₁dg + 1/2 dv₁² = P₂ + h₂dg + 1/2 dv₂²

Now,  h₁dg - h₂dg = 1000 × 10 × (5/100) = 500

  P₁ + 1/2 dv₁² + h₁dg - h₂dg = P₂ +  1/2 dv₂²

 P₁ - P₂ = 1/2d(v₂² - v₁²) +  h₂dg - h₁dg

 P₁ - P₂ = 1/2 × 1 (0.20² - 0.10²)  - 500

 P₁ - P₂ = 15 - 500 = -485 N/m²

P₂  - P₁ = 485 N/m².

Hope it helps.