Question

A long horizontal hose of diameter 3.8 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1 cm. Water squirts from the nozzle at velocity 18 m/sec. Assume that the water has no viscosity or other form of energy dissipation.

1)

What is the velocity of the water in the hose ?

m/s

2)

What is the pressure differential between the water in the hose and water in the nozzle ?

Pa

3)

How long will it take to fill a tub of volume 60 liters with the hose ?

sec

A rectangular block of ice 7 m on each side and 0.7 m thick floats in sea water. The density of the sea water is 1025 kg/m³. The density of ice is 917 kg/m³.

1)

How high does the top of the ice block float above the water level?

m

2)

How many penguins of mass 23 kg each can stand on the ice block before they get their feet wet?

Answer 1

A long horizontal hose of diameter 3.8 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1 cm. Water squirts from the nozzle at velocity 18 m/sec. Assume that the water has no viscosity or other form of energy dissipation.

1)

A₁V₁=A₂V₂

V₂=A₁V₁/A₂

V₂=[(π/4)(0.01m)²(18m/s)]/[(π/4)(0.038m)²]

V₂=1.25m/s

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2)

P₂-P₁=(1/2)( ρ)(V₁²-V₂²)

P₂-P₁=(1/2)( 1025kg/m³)[(18m/s)²-(1.25m/s)²]

P₂-P₁=165249.2Pa

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3)

Vol/t=V*A

t=Vol/(V*A)

t=(0.06m³)/(1.25m/s*1.13*10^-3m²)

t=42.44s

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A rectangular block of ice 7 m on each side and 0.7 m thick floats in sea water. The density of the sea water is 1025 kg/m3. The density of ice is 917 kg/m3.

1)

F_b=F_g

(1025)(34.3-49h)(g)=(917)(34.3)(g)

35157.5-50225h=31453.1

h=0.0738m

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2)

we will add 23x to the gravitational force of the ice (to the cancelled g part) and use the fully submerged volume of the ice on the left with the buoyancy force.
(1025)(34.3)=(917)(34.3) + 23x
X = 161 penguins