Water flows through a cylindrical pipe, whose inner diameter is 7 cm, at the rate of 6 km/h in an empty cylindrical tank, the radius of whose basis is 40 cm and height is 4.9 m. How long will it take to fill the whole tank ?
Answers
The cylindrical tank will be filled in 6 minutes 4 seconds.
Step-by-step explanation:
According to the question,
For cylindrical tank:
=> Radius of base of cylindrical tank, r₁ = 40 cm
So, diameter of base of cylindrical tank, D = r₁*2 = 40*2 = 80 cm
=> Height of the cylindrical tank, h₁ = 4.9 m = 4.9 * 100 = 490 cm
=> The rate of water flow = 6 km/h
60 min (1 hr) = 6000 m (6 km)
1 min = 6000 / 60 = 100 m or 10,000 cm
=> The Volume of cylindrical tank:
= πr₁²h₁
= π * 40 * 40 * 490
= 784 * 10³ π cm³ ...(1)
For cylindrical pipe:
=> Suppose the cylindrical tank is filled in x min. So, the length of water column = 10,000 x m
⇒ length or height of cylindrical pipe, h₂ = 10,000 x cm
=> Radius of pipe, r₂ = d/2 = 7/2 cm
=> Volume of cylindrical pipe :
= πr₂²h₂
= π * 7/2 * 7/2 * 10,000 x
= 1225 * 10² * x * π cm³ ...(2)
=> From eq (1) and (2), we get
784 * 10³ π cm³ = = 1225 * 10² * x * π cm³
x = 784 * 10³ π cm³ / 1225 * 10² π cm³
x = 7840 / 1225 cm³
x = 6.4
Thus, the cylindrical tank will be filled in 6 minutes 4 seconds.
Learn more:
Q:1 A cylindrical pipe has inner diameter of 4 cm and flows through it at the rate of 20 meter per minute. How long would it take to fill a conical tank of radius 40 cm and depth 72 m?
Click here : https://brainly.in/question/1123687
Q:2 Water flows through a cylindrical pipe of internal diameter 7cm at 5m/sec. Calculate the volume in litres, of water discharged by the pipe in one minute. Also calculate the time taken in minutes the pipe would take to fill an empty rectangular tank 4m*3m*2.31m
Click here : https://brainly.in/question/274084
Answer:Radius of base of cylindrical tank, r₁ = 40 cm
So, diameter of base of cylindrical tank, D = r₁*2 = 40*2 = 80 cm
= Height of the cylindrical tank, h₁ = 4.9 m = 4.9 * 100 = 490 cm
= The rate of water flow = 6 km/h
60 min (1 hr) = 6000 m (6 km)
1 min = 6000 / 60 = 100 m or 10,000 cm
= The Volume of cylindrical tank:
= πr₁²h₁
= π * 40 * 40 * 490
= 784 * 10³ π cm³ ...(1)
For cylindrical pipe:
= Suppose the cylindrical tank is filled in x min. So, the length of water column = 10,000 x m
length or height of cylindrical pipe, h₂ = 10,000 x cm
= Radius of pipe, r₂ = d/2 = 7/2 cm
= Volume of cylindrical pipe :
= πr₂²h₂
= π * 7/2 * 7/2 * 10,000 x
= 1225 * 10² * x * π cm³ ...(2)
= From eq (1) and (2), we get
784 * 10³ π cm³ = = 1225 * 10² * x * π cm³
x = 784 * 10³ π cm³ / 1225 * 10² π cm³
x = 7840 / 1225 cm³
x = 6.4 min
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Step-by-step explanation: