A 1,040 N force is recorded on a hemispherical vane as it redirects a 2.5 cm- blade diameter water jet through a 180 angle. Determine the velocity of the flowing water jet if the blade diameter water jer through a 180' angle. Determinethe velcity of the flowing water jet if is assumed to be frictionless.

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A 1,040 N force is recorded on a hemispherical vane as it redirects a 2.5 cm- blade diameter water jet through a 180 angle.

Determine the velocity of the flowing water jet if the blade is assumed to be frictionless.

the velocity of the flowing water jet is 32.55 m/s  assuming the blade is frictionless

Explanation:

Given that;

Force Ft = 1040 N

diameter d = 2.5 cm = 0.025 m

we know that; force acting on Hemispherical plate is;

Ft = 2δav²

where

a is area = π/4(0.025)²

δ is density of water = 1000 kg/m³

v is velocity = ?

now we substitute

1040 = 2 × 1000 × (π/4(0.025)²) × v²

1040 =  0.9817v²

v² = 1040 / 0.9817

v² = 1059.3867

v = √1059.3867

v = 32.5482 ≈ 32.55 m/s

Therefore the velocity of the flowing water jet is 32.55 m/s  assuming the blade is frictionless

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