Question

Water flows steadily through a horizontal pipe of a variable cross section. If the pressure of the water is $p$ at a point where the speed of the flow is $v$, what is the pressure at another point where the speed of the flow is $2v$ ; Let the density of water be

• A. $p + (3/2) \rho v^2 $
• B. $p - 2 \rho v^2 $
• C. $p + 2 \rho v^2 $
• D. $p - 3 \rho v^2 $
• E. $p - (3/2) \rho v^2 $

Answer 1

Answer: (E)

Two point are situated in a pipe and their height from ground is zero $(h=0)$.
$\because$ According Bernoulli's theorem,
$p+\rho g h+\frac{1}{2} \rho v^{2}=$ constant
At a point pressure of water is $p$ and speed of flow is $v$
therefore, $p+\frac{1}{2} \rho v^{2}=c$ ...(i)
At another point speed of flow is $2 v$ therefore,
$p_{1}+\frac{1}{2} \rho(2 v)^{2}=c$ ...(ii)
To find pressure $p_{1}$ at another point, equating the equation (i) and (ii)
$\Rightarrow p+\frac{1}{2} \rho v^{2}=p_{1}+\frac{1}{2} \rho\left(4 v^{2}\right)$
$\Rightarrow p_{1} =p-\frac{3}{2} \rho v^{2}$