Water is conveyed thourth a horizontal tube 8 cm in diameter and 4 kilometer in length at the rate of 20 litre/s Assumming only viscous resistance , callcalute the pressure required to maintain the flow . Coefficient of viscosity of water is 0.001 pa s
Answers
The pressure required to maintain the flow is 32 k pa
Explanation:
Given as :
The diameter of tube = 8 cm = 0.08 m
Radius of tube = 0.04 m
The length of the tube = l = 4 km = 4000 m
The rate of water discharge = 20 l/sec = 20000 ml/s
Coefficient of viscosity of water = 0.001 pa s
Let The pressure require to maintain the flow = P pascal
According to question
Volume of tube = V = π × r² × l
= 3.14 × (0.04)² × 4000
= 20.096 m³
∵ rate of water discharge = 20000 ml/s
So, Time of flow =
=
= 1 milli sec
So, Velocity of rush =
=
= 4 × m/s = 4000 km/s
Again'
work perform to push water through length of tube = P ×V
By conservation of energy
P V = × × V × v²
Or, P = 0.5 × 0.001 × ( 4000 )²
= 32000
= 32 k pa
So, The pressure required to maintain the flow = 32 k pa
Hence, The pressure required to maintain the flow is 32 k pa Answer
Water is conveyed thourth a horizontal tube 8 cm in diameter and 4 kilometer in length at the rate of 20 litre/s . Coefficient of viscosity of water is 0.001 pa s
Stepwise explanation is given below:
- It is given that,
The diameter of tube = 8 cm = 0.08 m
So, the Radius of tube = 0.04 m
- The length of the tube
= l = 4 km = 4000 m
The rate of water discharge
= 20 l/sec = 20000 ml/s
- Coefficient of viscosity of water
= 0.001 pa s
- Let The pressure require to maintain the flow = P pascal
- According to question
Volume of tube = V = π × r² × l
= 3.14 × (0.04)² × 4000
= 20.096 m³
- ∵ rate of water discharge = 20000 ml/s
So, time of flow = volume/rate
= 20.096 /20000
= 1milli sec
- So, velocity of rush = length of tube velocity / time od flow
4000/(10)^-3
=4 (10)^6. m/s =4000 km /s
- Now,
work perform to push water through length of tube = P ×V
- By conservation of energy
P V = × × V × v²
Or, P = 0.5 × 0.001 × ( 4000 )²
= 32000
= 32 k pa
- So, The pressure required to maintain the flow = 32 k pa