You visited us 27 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Dimensional Analysis

The mass of t...

Question

The mass of the liquid flowing per second per unit area of cross section of the tube if proportional to $P^{x}$ and $v^{y}$ , where $P$ is the pressure difference and $v$ is the velocity then the relation between $x$ and $y$ is

x = y

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = - y

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y^{2} = x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = - x^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $x = - y$
Given $m α P^{x} \times V^{y}$
$[{M L}^{- 2} T^{0}] = {[{M L}^{- 1} T^{- 2}]}^{x} {[M^{0} {L T}^{1}]}^{y}$
$x = 1$ } Comparing coefficients
$- 2 = - x + y$ and $- 1 = - 2 x - y$
$- 2 = - 4 x - 2 y$
$0 = (- 4 x - 2 y) - (- x + y)$
$0 = - 3 x - 3 y$
$\Rightarrow$ $3 x = - 3 y$ $\Rightarrow$ $x = - y$ .

Suggest Corrections

Similar questions

Q. The mass of the liquid flowing per second per unit area of cross section of a tube is proportional to

P^{x} a n d v^{y}

, where P is the pressure difference and v is the velocity. Then the relation between x and y is

Q. The mass of liquid flowing per second per unit area of cross section of the tube is proportional to

P^{x}

and

v^{y}

, where

P

is the pressure difference and

v

is the velocity, then the relation between

x

and

y

Q. The mass of the liquid flowing per second per unit area of cross section of a tube per unit time is proportional of

P^{x}

and

v^{y}

, where P is the pressure difference and v is the velocity. Then the relation between x and y if proportionality constant is dimensionless is

Q. The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)

^{n}

and (average velocity of the liquid )

^{m} .

Which of the following relations between

m

and

n

is correct ?

Water flows in a horizontal tube of variable cross section as shown. If the pressure difference of water between $X$ and $Y$ is $600 N / m^{2}$ , Area of cross section of pipe at $X$ and $Y$ are $3 c m^{2}$ and $1.5 c m^{2}$ respectively. Find the rate of flow of water through the tube. $($ Assume density of water as $1000 k g / m^{3}$ and $\frac{1}{\sqrt{10}} = 0.316)$

Join BYJU'S Learning Program

The mass of the liquid flowing per second per unit area of cross section of the tube if proportional to Px and vy, where P is the pressure difference and v is the velocity then the relation between x and y is

The correct option is B x=−yGiven mαPx×Vy[ML−2T0]=[ML−1T−2]x[M0LT1]yx=1 } Comparing coefficients−2=−x+y and −1=−2x−y −2=−4x−2y0=(−4x−2y)−(−x+y)0=−3x−3y⇒ 3x=−3y ⇒ x=−y.

The mass of the liquid flowing per second per unit area of cross section of the tube if proportional to $P^{x}$ and $v^{y}$ , where $P$ is the pressure difference and $v$ is the velocity then the relation between $x$ and $y$ is