Water flows through a tube shown in figure. The areas of cross section at A and B are 1 $c m^{2}$ and 0.5 $c m^{2}$ respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm $s^{-} 1$ , find (a) the speed at B and (b) the difference in pressures at A and B.

Open in App

Solution

(a) ${\to V}_{A} \times a_{A} = {\to V}_{B} \times a_{B}$

$\Rightarrow 10 \times 1 = {\to V}_{B} \times 0.5$

$\Rightarrow {\to V}_{B} = 20$ cm/sec

(b) $\frac{1}{2} ρ v_{A}^{2} + ρ g h_{A} + p_{A}$

= $\frac{1}{2} ρ v_{B}^{2} + ρ g h_{A} + p_{B}$

$\Rightarrow p_{B} - p_{A} = \frac{1}{2} ρ (v_{A}^{2} - v_{B}^{2}) + ρ g (h_{A} - h_{B})$

= $\frac{1}{2} \times 1 (100 - 400) + 1 \times 1000 (5.0)$

=- $150 + 5000 = 4850 \frac{Dyne}{c m^{2}}$

= 485 $N / m^{2}$

Suggest Corrections

Similar questions

Q. Water flows through a tube shown in figure. The area of cross section at A and B are 1 cm²and 0.5 cm² respectively. The height difference between A and B is 5 cm. If the speed of water at A is 10 cm s⁻¹ find (a) the speed at B and (b) the difference in pressures at A and B.

Water flows through a horizontal tube of variable cross section figure. The area of cross section at A and B are 4 $m m^{2}$ and 2 $m m^{2}$ respectively. If 1 cc of water enters per second through A, find (a) the speed of water at A, (b) the speed of water at B and (c) the pressure difference $P_{A} — P_{B}$ .