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 1 g cm- 3 .

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 1 g cm- 3 . (A) p+((3/2))ρ v2 (B) p-2ρ v2 (C) p-3ρ v2 (D) p-((3/2))ρ v2

Tardigrade Admin · Accepted Answer

Two point are situated in a pipe and their height from ground is same

∵

According Bernoulli's theorem,

p + ρ g h + \frac{1}{2} ρ v^{2} =

constant
At a point pressure of water is

p

and speed of flow is

v

therefore,

p + \frac{1}{2} ρ v^{2} = c

.....(i)
At another point speed of flow is

2 v

therefore,

p_{1} + \frac{1}{2} ρ (2 v)^{2} = c

......(ii)
To find pressure

p_{1}

at another point, equating the equation (i) and (ii)

\Rightarrow p + \frac{1}{2} ρ v^{2} = p_{1} + \frac{1}{2} ρ (4 v^{2})

\Rightarrow p_{1} = p - \frac{3}{2} ρ v^{2}

Q. 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 $2 v$ ? Let the density of water be $1 g c m^{- 3}$ .

$p + (\frac{3}{2}) ρ v^{2}$

$p - 2 ρ v^{2}$

$p - 3 ρ v^{2}$

$p - (\frac{3}{2}) ρ v^{2}$

$p - (\frac{5}{2}) ρ v^{2}$

Q. 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 1gcm−3 .

p+(23​)ρv2

p−2ρv2

p−3ρv2

p−(23​)ρv2