Water flows through a circular pipe whose internal diameter is 2 cm at the rate of 6 m/sec into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level in water in 30 minutes
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Answers
Step-by-step explanation:
EXPLANATION.
Water flows through a circular pipe.
Internal diameter = 2 cm.
Rate = 6m/sec into a circular tank.
The radius of whose base = 60 cm.
To find the rise in the level in water in 30 minutes.
As we know that,
Diameter = 2 x Radius.
Radius = Diameter/2.
Radius = 2/2 = 1 cm = 1/100 m.
Volume of cylinder = πr²h.
Volume of water flows through a circular pipe in 1 seconds = πr²h.
π x (1/100)² x 6.
The raise in the water level in 30 minutes = π x (1/100)² x 6 x 30 x 60.
Radius whose base = 60 cm = 60/100 m.
Volume = πr²h.
⇒ π x (60/100)² x h.
⇒ π x (60/100)² x h = π x (1/100)² x 6 x 30 x 60.
⇒ 60/100 x 60/100 x h = 1/100 x 1/100 x 6 x 30 x 60.
⇒ 60 x 60 x h = 6 x 30 x 60.
⇒ 60 x h = 6 x 30.
⇒ 10 x h = 30.
⇒ h = 3m.
GIVEN :
Internal diameter is = 2 cm
water flow rate thought of pipe = 6 m/sec
Radius of tank is = 60 Cm
Time = 30 min
The volume of water that flows for 1 Sec thought the pipe at the rate of 6 m / sec is nothing but the cylinder with h = 6
Also, given is the diameter which is 2 cm therefore,
r = 1 / 100 m
Volume of water flow for 1 Sec
22/7 × 1/100 × 1/100 × 6
Now, Find the volume of water that flows for 30 min into sec
it will be 30×60
Volume of water that flows for 30 cm
= 22/7 × 1/100 × 1/100 × 6 × 30 × 60
let the radius of tank be " R "
R = 60 cm
R = 60/100
Volume of water collected in the tank after 30 min = Volume of water that flows through the pipe for 30 min
22/7 × 60/100 × 60/100 × h = 22/7 × 1/100
h = 3 m
∴ the High of the tank is 3 metre