Fluid Dynamics Homework: Solving for Water Speed and Range in a Container

[azure2s]

Homework Statement

A container has spouts 10 cm, 20 cm, 30 cm, and 40 cm. The water level is maintained at a 45 cm height by an outside supply. (a) what is the speed of the water out of each hole? (b) which water stream has the greatest range relative to the base of the container?

Homework Equations

Bernoulli's Equation: p₁ + 1/2desnityv₁² + pgy₁ = p₂ + 1/2densityv₂² + pgy₂

The Attempt at a Solution

I tried to first solve the the spout 40 cm high. Using the equation, the pressure and density gets canceled, so we have:

v₁² - v₂² = 2g(y2 - y1)

since v₂ = 0, then

v₁ = square root of 2g(y₂ - y₁)

v1 = square root of 2(9.8)(45 - 40)
v1 = 9.9

But my answer is wrong according to my teacher... :( Hope you can help me

 

[LowlyPion]

Homework Statement

A container has spouts 10 cm, 20 cm, 30 cm, and 40 cm. The water level is maintained at a 45 cm height by an outside supply. (a) what is the speed of the water out of each hole? (b) which water stream has the greatest range relative to the base of the container?

Homework Equations

Bernoulli's Equation: p₁ + 1/2desnityv₁² + pgy₁ = p₂ + 1/2densityv₂² + pgy₂

The Attempt at a Solution

I tried to first solve the the spout 40 cm high. Using the equation, the pressure and density gets canceled, so we have:

v₁² - v₂² = 2g(y2 - y1)

since v₂ = 0, then

v₁ = square root of 2g(y₂ - y₁)

v1 = square root of 2(9.8)(45 - 40)
v1 = 9.9

But my answer is wrong according to my teacher... :( Hope you can help me

Your height difference is measured in cm not m.

 

[azure2s]

Your height difference is measured in cm not m.

LOL! I can't believe that was the only mistake I did! Thank you very much! =)) Now my answer is the same with my teacher's.

 

[LowlyPion]

LOL! I can't believe that was the only mistake I did! Thank you very much! =)) Now my answer is the same with my teacher's.

Good luck.