# Homework Help: Cowboy filling trough problem

1. Apr 11, 2005

### imnotsmart

A cowboy at a dude ranch fills a horse trough that is 1.7 m long, 65 cm wide, and 35 cm deep. He uses a 2.2 cm diameter hose from which water emerges at 1.4 m/s. How long does it take him to fill the trough?

I know the trough's volume is .387m^3.
How do I find the rate at which the water fills?

2. Apr 11, 2005

### stunner5000pt

$\mbox{mass rate flow = a constant =} \ R_{V}= Av$

A is the corss sectional area, p is the density of the fluid (water = 1), and v is the velocity at the flow is going
Rv is going to come in m^3/s
now you have the Volume in m^3, and the flow is m^3/s
then obviously $$R_{V} t = V$$

3. Apr 11, 2005

### imnotsmart

How do I go about finding how long it takes.

4. Apr 11, 2005

### stunner5000pt

perhaos i was being UNCLEAR

the RATE OF FLOW is given by the Cross section area from which the fluid comes out from times the VELOCITY at whiuch the fluid flows out

thus $R_{V} = Av$
what are teh UNITS of Rv???

by unit elimination you'll figure that
rate of flow x time = volume

5. Apr 11, 2005

### imnotsmart

So 1.4 m/s * time= .387m
which =.28s?

6. Apr 11, 2005

### stunner5000pt

what is the rate of flow(given as Rv)?? $R_{V} = \mbox{AREA x VELOCITY}$

and then the RATE OF FLOW times the time gives you the volume

that is Rv (the rate of flow) x t (time) = Volume
isolate for time (t) and solve

7. Apr 11, 2005

### imnotsmart

Don't think i totally sound stupid here but am i looking for the area of the hose?

8. Apr 11, 2005

### stunner5000pt

area of the cross section i.e. if you cut the hose like it was a sausage that was being cut horizontally then find the area of that circular face

9. Apr 11, 2005

### imnotsmart

so 3.8e-4 is the area and the volume is .387

Last edited: Apr 11, 2005
10. Apr 11, 2005

### imnotsmart

I figured it out...the answer is 12.1 min...thanks buddy