(a) The speed of the water at point B is 10 m/s and the speed at point C is 5 m/s.
(b) The pressure of the water at point B is 4.96 bars and the pressure at point C is 5.335 bars.
Speed of the water at point B
The speed of the water at point B is determined from continuity equation as shown below;
Q = AV
A₁V₁ = A₂V₂
Since, A₁ = A₂ = 3 m²
V₁ = V₂ = 10 m/s
Thus, the speed of the water at point B is 10 m/s.
Speed of water at point C
A₁V₁ = A₃V₃
A₁V₁ = (2A₁)V₃
V₃ = (A₁V₁) / 2A₁
V₃ = V₁ / 2
V₃ = 10/2
V₃ = 5 m/s
Thus, the speed of the water at point C is 5 m/s.
Pressure of the water at point B
The pressure of the water at point B is determined by appying Bernoulli's equation as shown below;
P₁ + ¹/₂ρV₁² + ρgh₁ = P₂ + ¹/₂ρV₂² + ρgh₂
where;
- P₁ = 3 bars = 300,000 Pa
- ρ density of water = 1000 kg/m³
- g is acceleration due to gravity = 9.8 m/s²
300,000 + ¹/₂(1000)(10)² + (1000)(9.8)(20) = P₂ + ¹/₂(1000)(10)²
546,000 = P₂ + 50,000
P₂ = 496,000 Pa
P₂ = 4.96 bars
Pressure of the water at point C
P₁ + ¹/₂ρV₁² + ρgh₁ = P₃ + ¹/₂ρV₃² + ρgh₃
546,000 = P₃ + ¹/₂(1000)(5)²
546,000 = P₃ + 12,500
P₃ = 533,500 Pa
P₃ = 5.335 bars
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