Did I do this fluids problem right? A find the gallons/min gushed by a fountain

[lalalah]

1. A fountain sends a stream of water straight up into the air to a maximum height of 4.23 m. The effective area of the pipe feeding the fountain is 5.38 x 10^-4 m^2. Neglecting air resistance and any viscous effects, determine how many gallons per minute are being used by the fountain. (1 gal = 3.79 x 10^-3 m^3)

Homework Equations

F = (mv^2)/r
F = P * A
P = density * g * h
m = density*(Ah)

The Attempt at a Solution

P= 1.013x10^5 * pgh
P= 1000*9.8*4.23 + 1.013x10^5
P= 142754 Pa

PA = F
PA = (mv^2)/r

r = (Area/pi)^(1/2)
r= .013086 m

mass = 1000 * area * 4.23
mass = 2.27574 kg

142754 Pa * (5.38 *10^-4 m^2) = (2.27574 kg * v^2)/.013086 m
v = .66455 (m/s multiply by area

.66455 * (5.38 * 10^-4) = .0001926 m^3/s

divide v by 3.79 * 10^-3 m^3, then multiply by 60 seconds

5.66 gal/min



this is so obviously wrong, but I've tried this prob beyond five times already and am at wits end... can anyone steer me in the right direction? thankkkks!

 

[Redbelly98]

F = (mv^2)/r

That equation isn't relevant here, since it applies to circular motion and centripetal force.

How about trying energy conservation?

 

[thomate1]

I cannot determine if your solution is correct without seeing your work and calculations. However, I can provide some guidance to help you check your work.

First, it's important to carefully read and understand the problem. In this case, the problem is asking for the gallons per minute of water being used by the fountain, not the velocity or force of the water. So your final answer should be in units of gallons per minute.

Next, make sure you are using the correct equations and units. The equations you listed are relevant, but you need to choose the appropriate ones for the problem. For example, the equation F = (mv^2)/r is used to calculate the centripetal force on an object moving in a circular path. This may not be relevant to the problem at hand.

Also, pay attention to units and make sure they are consistent throughout your calculations. For example, in your calculation for mass, you used the density of water in kg/m^3, but then you converted the volume to m^3/s, which is not a unit of volume. This could be why your final answer is off.

Finally, check your calculations and make sure they are correct. A small mistake in one step can throw off your final answer. If you are still having trouble, try breaking down the problem into smaller, simpler steps and double check each step as you go. And always make sure your answer makes sense in the context of the problem.

I hope this helps and good luck with your problem!