how long would it take to fill a conical vessel ?

Question

water flows at the rate of 10 meters per minute through a cylindrical pipe whose internal radius is 0.5 cm how long would it take to fill a conical vessel whose radius at the top is 20cm and depth is 21 cm?

Answer 1

Volume of a cone = (1/3)(BaseArea)(Height)
V = 1/3 (2pi (0.2)^2 )(0.21) = 0.01759 m^3


Volume of cylinder of water per minute
V = Area of circle (pipe) * height
V = 2pi ( 0.005)^2 (10)
V = 0.00157 m^3 / min

Fill up time = .01759 / .00157 = 11.198 minutes

Answer 2

Right, let's look at the volume of water coming in first:-

Area of pipe = pi*r^2; r=0.5 Therefore area = 0.785 sq cm.
The water is flowing at 10 m/s = 1000cm/s (to get the units all the same)
So volume of water coming in is:- 0.785*1000 cu cms/ sec
=785 cu cms / sec

Now the volume of the cone.

Vol of cone = pi*r^2*h/3. ie pi*400*21/3 = 8,796.452 cu cm

So if we divide the volume to be filled by the rate at which water is flowing, then we get the time taken.

8796.452/785 = 11.2 seconds.

That help?

Answer 3

Find the volume of water per minute:
R = 0.5 cm
L = 10 m = 1,000 cm
V/min = pi*R^2*L/min
V/min = pi * 250 cc / min

Find the volume of the cone:
r = 20 cm
H = 21 cm
C = 1/3 * pi * r^2 * h
C = pi * 2,800 cc

Find the time to fill the cone:
T = C / (V/min) or
T= pi * 2,800 cc / (pi * 250 cc / min)
T = (2,800 / 250) min
T = 11.2 minutes

Answer 4

volumeflowing /sec from cylindrical pipe=pi(0.5)^2*1000/60
=13.09cm^3/sec
volume of conical vessel=1/3pi(020)^2* 21= 8796.46cm^3
time required=08796.46/1309 sec.=672secs
=.11.2minANS