The speed of water at the other place where the pressure is half of that at the first place is 10 m/s.
How to calculate the speed of water at the other place?
The speed of water at the other place where the pressure is half of that at the first place is calculated by applying Bernoulli's equation as follows.
P₁ + ¹/₂ρv₁² = P₂ + ¹/₂ρv₂²
where;
- P₁ is the pressure in first place
- P₂ is the pressure in second place
- ρ is the density of water
- v₁ is the speed of water in first place
- v₂ is the speed of water in second place
The given parameters include;
P₁ = 10 N/cm² = 100,000 N/m²
v₁ = 30 cm/s = 0.3 m/s
ρ = 1000 kg/m³
P₂ = ¹/₂P₁ = 50,000 N/m²
v₂ = ?
100,000 + ¹/₂(1000)(0.3)² = 50,000 + ¹/₂(1000)v₂²
50,045 = 500v₂²
v₂² = 50,045 / 500
v₂² = 100.09
v₂ = √100.09
v₂ = 10 m/s