The pipe near the lower end of a large storage tank develops a small leak and a stream of water shoots from it. The top of water tank is 15 m above the point of leak.
(a) With what speed does the water rush from the hole?
 (b) If the hole has an area of 0.060 cm² how much water flows out in one second?
(Ans: (a) 17 m s⁻¹, (b) 102 cm³)


Data Given:

Height of tank = h = 15 m 

Area of the hole = A = 0.060 cm² = 6.0 ï½˜ 10⁻⁶ m²


To Find:


(a) Speed of the water  = v = ? 
(b) The volume discharged per second = `\frac {ΔV}{Δt}` = ?


Solution:

(a) Speed of the water  = v = ? 

The speed of water rushes out from the hole can be calculated by the Torricelli's Theorem

v = `\sqrt {2gh}`

by putting values 

v = `\sqrt {2 ｘ 9.8m s⁻² 15.0 m}`

v = `\sqrt {294 m² s⁻²}`

v = 17.146 m s⁻¹

v = 17 m s⁻¹ ----------Ans.(1)


(b) the volume discharged per second = `\frac {ΔV}{Δt}` = ?

From the the equation of continuity the rate of volume flow is given by the relation

`\frac {ΔV}{Δt}` = A v

`\frac {ΔV}{Δt}` =  6.0 ï½˜ 10⁻⁶ m² ï½˜ 17 m s⁻¹

`\frac {ΔV}{Δt}` =  102 ï½˜ 10⁻⁶ m³ s⁻¹

or

`\frac {ΔV}{Δt}` =  102 cm³ s⁻¹ ------------Ans.(2)


Similar Questions:





************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.