Bernoulli's Equation and stream of water

[knightassassin]

Homework Statement

The figure below shows a stream of water in a steady flow from a kitchen faucet. At the faucet the diameter of the stream is 1.20 cm. The stream fills a 125 cm3 container in 18.2 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. (The answer should be in cm)

Homework Equations

A1v1=A2v2 and P1+0.5densityv^2+density(gh)=P2+0.5(density)v^2+density(gh)

The Attempt at a Solution

Not sure how to attempt this problem. I found the speed at which the water flows
I used the rate (125cm3/18.2)/(0.6^2)pi=6.078 cm/s, but not sure if this information is relevant or not

 

[Chi Meson]

This can be done without the Bernoulli equation. Assuming the stream does not break up, the volume flow rate should remain constant. The speed will increase according to simple conservation of energy (potential to kinetic). Actually, that's all Bernoulli's eq is, conservation of energy-per-unit-volume.

After finding the final speed, find the necessary diameter of the stream to provide the same volume flow rate you started with.

 

[tomcue]

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I would approach this problem by using Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a steady flow. In this case, we are given the diameter of the stream at one point and the time it takes to fill a container, which can be used to calculate the speed of the stream. This information can then be used in the equation to find the pressure at the two points (at the faucet and 13 cm below the faucet) and ultimately, the diameter of the stream at the lower point.

Using the equation A1v1 = A2v2, we can find the velocity at the lower point by rearranging to v2 = (A1v1)/A2. Plugging in the values, we get v2 = (1.20 cm x 6.078 cm/s)/(A2). We can then use this velocity in the equation P1 + 0.5densityv^2 + density(gh) = P2 + 0.5(density)v^2 + density(gh) to find the pressure at the two points.

Solving for A2, we get A2 = (1.20 cm x 6.078 cm/s)/v2 = 7.294 cm^2. Since the area of a circle is A = πr^2, we can rearrange to find the radius, which is equal to half the diameter. Thus, the diameter at the lower point is (2 x 7.294 cm^2/π)^1/2 = 1.71 cm.

Therefore, the diameter of the stream 13.0 cm below the opening of the faucet is approximately 1.71 cm.