Answer:
31.6 m/s
Explanation:
Mass is conserved, so the mass flow at the outlet of the pump equals the mass flow at the nozzle.
m₁ = m₂
ρQ₁ = ρQ₂
Q₁ = Q₂
v₁A₁ = v₂A₂
v₁ πd₁²/4 = v₂ πd₂²/4
v₁ d₁² = v₂ d₂²
Now use Bernoulli equation:
P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂
Since h₁ = 0 and P₂ = 0:
P₁ + ½ ρ v₁² = ½ ρ v₂² + ρgh₂
Writing v₁ in terms of v₂:
P₁ + ½ ρ (v₂ d₂²/d₁²)² = ½ ρ v₂² + ρgh₂
P₁ + ½ ρ (d₂/d₁)⁴ v₂² = ½ ρ v₂² + ρgh₂
P₁ − ρgh₂ = ½ ρ (1 − (d₂/d₁)⁴) v₂²
Plugging in values:
579,160 Pa − (1000 kg/m³)(9.8 m/s²)(15 m) = ½ (1000 kg/m³) (1 − (1.99 in / 3.28 in)⁴) v₂²
v₂ = 31.6 m/s
Jack Nicklaus once said about golf that "hitting a perfectly straight shot with a big club is a fluke." Science of Golf (SOG): Newton’s Third Law of Motion and Momentum explains what happens when a golfer swings a golf club and applies a big force to the small golf ball. The video features amateur golfer and Stanford University student Patrick Rodgers who gives his opinion on the importance of knowing what causes power and speed in the golf swing. Jim Hubbell, research engineer at the United States Golf Association (USGA) discusses what forces are and how they work in pairs. Hubbell also defines momentum and how it is transferred to the ball.
Hope this helps
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