M4maths Previous Puzzles

14 Apr 2016 Rate of flow in kilometer

A cylindrical pipe has inner diameter of 7 cm and water flows through it at 192.5 litre per minute. Find the rate of flow in kilometers per hours.

OPtion

1) 1 km/hr
2) 2.5 km/hr
3) 3 km/hr
4) 3.5 km/hr
5) 4 km/hr
6) 5 km/hr
7) 5.5 km/hr
8) 6 km/hr
9) 7 km/hr
10)7.5 km/hr

Solution

Volume of water that flows per hour = (192.5 * 60) litre
= 192.50*60*1000 cm^3 ....(i)
Inner diameter of the pipe = 7 cm
Inner radius of the pipe = 7/3 cm = 3.5 cm
Let h cm be the length of the column of water that flows in one hour
Clearly, water column is a cylinder of radius 3.5 cm and length h cm.
therefore
Volume of water that flows in 1 hours
= Volume of cylinder of radius 3.5 cm and length h cm
= 22/7 * 3.5^2 * h cm^3 ....(ii)
From (i) and (ii), we get
22/7 * 3.5*3.5*h = 192.50*60*1000
h = 300000 cm
= 3 km
Hence, the rate of flow of water is 3 km per hour.
Option 3)

Correct Option: 3 Best Solution (10)

ABHINAV PUSHPAM   8 years AGO

Diameter of Cylinder = 7cm therefore radius of cylinder = diameter/2 = 7/2 = 3.5cm . One Liter = 1000cm^3 , therefore, 192.5 litre = 192.5 *1000cm^3 = 192500 cm^3
now in 1minute it collects 192500cm^3 of water so in 1hour it collects 192500*60(1hour=60minutes)
now we have to find out the height ( rate of flow is same as height)
since, volume of cylinder =3.14*r^2*h
so, 22/7*3.5*3.5*h=192500*60
h=300000cm =3km
hence, rate of flow =3km per hour
Option 3)

Like? Yes (27) | No (4)  

Kalpana   8 years AGO

given diameter=7cm
so radius=7/2=3.5cm
one litre=1000cm^3
192.5litre=192.5*1000cm^3=192500
1hr=60min
to convert into hr
192500*60=11550000
vol=?*r*r*h
h=11550000/3.5*3.5*3.14
h=3km/hr

Like? Yes (10) | No (5)  

Aakash Beniwal   8 years AGO

Radius of pipe=7/2 cm
Volume of water flow in 1 minute=192.5 L.... (1)
in 1 hour=192.5 *60 *1000 cm^3
let h be distance covered by water in 1 hour.
volume of water that covers in 1 hrs= pi * r^2 *h.... (2)
solve by putting eq(1) =eq(2)
finh vale of h, which is distance covered in per hour

Like? Yes (7) | No (5)  

RAHUL KUMAR   8 years AGO

Diameter of cylindrical pipe = 7
cm
∴ Radius of cylindrical pipe = 7/2 cm
Volume of water flows in 1 min =
192.5 l
∴ Volume of water flows in 1
hour = 192.5 × 60 × 1000 cm3
......(1)
Let l be the distance covered by
water in 1 hour
Volume of water that covers the
diameter of 1 hour = πr2 l ..... (2)
(1) and (2) ⇒ πr2 l = 192.5 × 60
× 1000
π*(7/2)^2*l = 192.5*60*100
l = 300000 cm
l = 3 Km.
i.e. distance covered by water in
1 hr is 3 km (1km = 100000 cm)
∴ Rate of flow of water = 3 km/hr

Like? Yes (4) | No (3)  

SANTOSH KUMAR DASH   8 years AGO

radius of the pipe=7/2 cm=3.5 cm
volume of water filled in 1min=192.5 litrs/min=192.5*1000 cm^3/min
volume of water filled in 1 hour=192.5*1000*60 cm^3/hour
let the length of water flowing through the pipe in 1 hour be 'l' mitres
volume of water that flows through the pipe=22/7*(3.5)^2*l
=>(22/7)*(3.5)^2*l=192.5*1000*60
=>l=192.5*1000*60*(7/22)*(1/(3.5^2))
=>l=300000cm
=>l=3000m=3km

so flow rate=3km/hr(option 3)

Like? Yes (4) | No (3)  

Yashi Das   8 years AGO

area=pi*(r^2)
= (22/7)*(7/2)*(7/2)=38.5 cm^2
volumetric flow rate=192.5 l/min =192.5*1000 cm^3/min
1 l= 1 dm ^3 =1000 cm^3
therefore,
flow rate = 192.5*1000 /38.5 =5000 cm/min =5000*0.00001 km/(1/60 h) = 3 km/hr

Like? Yes (2) | No (2)  

praveenkumar   8 years AGO

first of alla we have to find out the raddi that equals to3.5cm
now convert 192.5litr in to cm raht equals (1000cm^3=1litr) so there are 192500cm
now in 1min it collects 192500cm^3 of water so in 1hr it collects 192500*60
now we have to find out the height
so volume of cylinder=3.14*r^2*7
so 22/7*3.5*3.5*h=192500*60
h=300000cm=3km

Like? Yes (3) | No (3)  

Lenin   8 years AGO

rate of flow, V = Q/A
Q (discharge) = 192.5 litre = 0.1925 m^3
A (cross sectional area) = 3.14*7*7/4 = 38.485 cm^2 = 0.00384 m^2
so, V = 0.1925/0.00384 = 50 m/min = 3 km/hr
so, option 3.

Like? Yes (6) | No (6)  

Juned A Hashmi   8 years AGO

Area of cross section = 77/2 square cm
1 litre = 1000 cubic cm
length of the flow per hour = (192500 x 60 x 2)/77
in km/hr = 300000/100000 = 3 km/hr

Like? Yes (2) | No (4)  

Akshat Sood   8 years AGO

after finding height comes out to be=5000cm
Speed =5000*60/100000=3km/hr

Like? Yes (2) | No (6)