Question 161: Properties of Matter

Question

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm
–2
between A and B where the area of cross section
are 40 cm
2
and 20 cm
2
, respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm
–3
)

Accepted Answer

Rate of flow of water is same at both A and B
A
A
V
A
= A
B
V
B
(40)V
A
= (20)V
B
V
B
= 2V
A
.......(1)
Using Bernoulli's theorem
P
A
+ $${1 \over 2}ho V_A^2$$ = P
B
+ $${1 \over 2}ho V_B^2$$
$$ \Rightarrow $$ P
A
- P
B
= $${1 \over 2}ho V_B^2$$ - $${1 \over 2}ho V_A^2$$
$$ \Rightarrow $$ 700 = $${1 \over 2} 	imes 1000\left( {4V_A^2 - V_A^2} ight)$$
$$ \Rightarrow $$ V
A
= 0.68 m/s = 68 cm/s
$$ 	herefore $$ Flow rate = A
A
V
A
= (40)(68) = 2720 cm
3
/s

Answer

1810 cm
3
/s

Answer

2420 cm
3
/s

Answer

3020 cm
3
/s

Answer

2720 cm
3
/s

Properties of Matter

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm –2 between A and B where the area of cross section are 40 cm 2 and 20 cm 2 , respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm –3 )

Choose the correct answer: