The flowing water through a cylindrical pipe with internal diameter 7

1.	The flowing water through a cylindrical pipe with internal diameter 7 cm at the speed of 192.5 liter per minute is collecting in a vessel. Find the speed of water in km/h \(\left( \pi =\frac { 22 }{ 7 } \right) \)
Answer» Given, Diameter of cylindrical pipe = 7 cm ∴ Radius (r) = \(\frac { 7 }{ 2 }\) = 3.5 cm = 0.035 m and the volume of flowing water in one minute = 192.5 liter ∴ The volume of flowing water in one hour = 192.5 × 60 liter = \(\frac { 192.5\times 60 }{ 1000 } \) m³ = 11.55 m³ …….(i) Let the speed of the water in pipe be x km./h ∴ Length of flowing water in one hour (h) = x m ∴ Volume of water flowing in one hour = πr²h = \(\frac { 22 }{ 7 }\) × (0.035)² × x = 0.00385 × x m³ …….(ii) From equation (i) and (ii) we get 0.00385 × x = 11.55 ⇒ x = \(\frac { 11.55 }{ 0.00385 }\) ⇒ x = \(\frac { 1155000 }{ 385 }\) ⇒ x = 3000 m = \(\frac { 3000 }{ 1000 }\) km = 3 km Hence the speed of water in the pipe = 3 km/h

The flowing water through a cylindrical pipe with internal diameter 7 cm at the speed of 192.5 liter per minute is collecting in a vessel. Find the speed of water in km/h \(\left( \pi =\frac { 22 }{ 7 } \right) \)

Answer»

Given,

Diameter of cylindrical pipe = 7 cm

∴ Radius (r) = \(\frac { 7 }{ 2 }\) = 3.5 cm = 0.035 m and the volume of flowing water in one minute = 192.5 liter

∴ The volume of flowing water in one hour

= 192.5 × 60 liter

= \(\frac { 192.5\times 60 }{ 1000 } \) m³

= 11.55 m³ …….(i)

Let the speed of the water in pipe be x km./h

∴ Length of flowing water in one hour (h) = x m

∴ Volume of water flowing in one hour = πr²h

= \(\frac { 22 }{ 7 }\) × (0.035)² × x

= 0.00385 × x m³ …….(ii)

From equation (i) and (ii) we get

0.00385 × x = 11.55

⇒ x = \(\frac { 11.55 }{ 0.00385 }\)

⇒ x = \(\frac { 1155000 }{ 385 }\)

⇒ x = 3000 m

= \(\frac { 3000 }{ 1000 }\) km = 3 km

Hence the speed of water in the pipe = 3 km/h