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,
$p+\rho gh+\frac{1}{2}\rho v^2=$ 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 $2v$ therefore,
$p_1+\frac{1}{2}\rho (2v{)}^2=c$ ...(ii)
To find pressure $p_1$ at another point, equating the equation (i) and (ii)
$\Rightarrow p+\frac{1}{2}\rho v^2=p_1+\frac{1}{2}\rho \left(4v^2\right)$
$\Rightarrow p_1=p-\frac{3}{2}\rho v^2$