Question

Water flows in a horizontal tube (see figure). The pressure of water changes by $700N/m^2$ between $A$ and $B$ where the area of cross sections are $40c{m}^2$ and $20c{m}^2$, respectively. Find the rate of flow of water through the tube. (density of water $1000kg/m^3$)

• A. $2420c{m}^3/s$
• B. $2720c{m}^3/s$
• C. $3020c{m}^3/s$
• D. $1810c{m}^3/s$

Answer 1

The correct option is B $2720c{m}^3/s$

We know that $A_A{v}_A=A_B{v}_B$

Using equation of continuity

Rate of flow of water $=A_A{v}_A=A_B{v}_B$

$\left(40\right)v_A=\left(20\right)v_B$

$v_B=2v_A$

Now, Using Bernoulli's theorem
$P_A+\frac{1}{2}\rho v_A^2=P_B+\frac{1}{2}\rho v_B^2$

$P_A-P_B=\frac{1}{2}\rho (v_B^2-v_A^2)$

$700=\frac{1}{2}\times 1000(4v_A^2-v_A^2)$

$v_A=0.68m/s=68cm/s$
And rate of flow=$A_A{v}_A$

$=\left(40\right)\left(68\right)$

$2720c{m}^3/s$
Final answer (c)