A man and women were gardening one night. The wife was watering the garden when she put her finger over the hole of the hose. The husband was curious about why it happened. Please explain in physics form why the phenomenon happened. I am doing this for a math extra. Could someone please help me find the solution to this problem.
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Think of it like this...
At any given moment, the amount of water entering the hose from its source is equal to the amount of water exiting it at the hole that the wife is covering up. This means:
A1V1=A2V2 ---> volume of liquid/unit time is constant in this case
Lets just give these values a couple numbers that are easy to work with.
A1=2cm^2
V1=100cm/s
A2=1cm^2 -----> We are assuming that she is covering up 1/2 of the opening at the end of the hose with her finger
Plug these values in to solve for V2
2(100)=1V2
V2=200cm/s
Since we lessened the area of the hole, the water must escape at a greater velocity in order to allow a constant volume of water to enter at the source at any given time. In fact, we can say that the velocity of the water exiting the hose is inversely proportional to the cross-sectional area that it may exit from. This concept applies to every point along the hose, so you can actually figure out the velocity of the liquid in any section of the hose if you know the volume/unit time that it is entering the hose and the cross-sectional area at that given segment.
I hope this helps!
At any given moment, the amount of water entering the hose from its source is equal to the amount of water exiting it at the hole that the wife is covering up. This means:
A1V1=A2V2 ---> volume of liquid/unit time is constant in this case
Lets just give these values a couple numbers that are easy to work with.
A1=2cm^2
V1=100cm/s
A2=1cm^2 -----> We are assuming that she is covering up 1/2 of the opening at the end of the hose with her finger
Plug these values in to solve for V2
2(100)=1V2
V2=200cm/s
Since we lessened the area of the hole, the water must escape at a greater velocity in order to allow a constant volume of water to enter at the source at any given time. In fact, we can say that the velocity of the water exiting the hose is inversely proportional to the cross-sectional area that it may exit from. This concept applies to every point along the hose, so you can actually figure out the velocity of the liquid in any section of the hose if you know the volume/unit time that it is entering the hose and the cross-sectional area at that given segment.
I hope this helps!