Water flows through a horizontal pipe of diameter 2 cm at a speed of 3 cm s-1, The pipe has a nozzle of diameter 0.5 cm at its end. The speed of water emerging from the nozzle is

Question

Water flows through a horizontal pipe of diameter 2 cm at a speed of 3 cm s-1, The pipe has a nozzle of diameter 0.5 cm at its end. The speed of water emerging from the nozzle is (A) 6 cm s-1 (B) 48 cm s-1 (C) 16 cm s-1 (D) 12 cm s-1

Tardigrade Admin · Accepted Answer

According to the equation of continuity, A v= constant Or A1 U1=A2 V2 (π × d12/4) V1=(π d22 V2/4) or V2=V1 ⋅((d1/d2))2 =3((2/0.5))2=48 cm / s

Q. Water flows through a horizontal pipe of diameter $2 c m$ at a speed of $3 c m s^{- 1}$ , The pipe has a nozzle of diameter $0.5 c m$ at its end. The speed of water emerging from the nozzle is

$6 c m s^{- 1}$

$48 c m s^{- 1}$

$16 c m s^{- 1}$

$12 c m s^{- 1}$

$36 c m s^{- 1}$

According to the equation of continuity,
$A v =$ constant
Or $A_{1} U_{1} = A_{2} V_{2}$
$\frac{π \times d _{1}^{2}}{4} V_{1} = \frac{π d _{2}^{2} V _{2}}{4}$
or $V_{2} = V_{1} \cdot (\frac{d _{1}}{d _{2}})^{2}$
$= 3 (\frac{2}{0.5})^{2} = 48 c m / s$

Q. Water flows through a horizontal pipe of diameter 2cm at a speed of 3cms−1, The pipe has a nozzle of diameter 0.5cm at its end. The speed of water emerging from the nozzle is

6cms−1

48cms−1

16cms−1

12cms−1

36cms−1

According to the equation of continuity, Av= constant Or A1​U1​=A2​V2​ 4π×d12​​V1​=4πd22​V2​​ or V2​=V1​⋅(d2​d1​​)2 =3(0.52​)2=48cm/s