An incompressible fluid of density - flows through a horizontal pipe of radius r and then passes through a constriction of radius r-2 - If the fluid has pressure Po and velocity Vo before the constriction- pressure in the constriction is Po-3-2- Vo2- Here - is an integer- Find - -

By equation of continuity, π r^2V_o=πr^2/4V V=4V_o By Bernoulli's equation, P_o+1 /2ρ V_o^2=P+1 /2ρ V^2 P_o+1 /2ρ V_o^2=P+1 /216ρ V_o^2; P=P_o 15 /2ρ V_o^2 n ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Body in Water

An incompress...

Question

An incompressible fluid of density $ρ$ flows through a horizontal pipe of radius r and then passes through a constriction of radius $\frac{r}{2}$ . If the fluid has pressure $P_{o}$ and velocity $V_{o}$ before the constriction, pressure in the constriction is $P_{o} - \frac{3 α}{2} ρ V_{o}^{2}$ . Here $α$ is an integer. Find $α$ .

Open in App

Solution

By equation of continuity,
$π r^{2} V_{o} = π \frac{r^{2}}{4} V$
$V = 4 V_{o}$
By Bernoulli's equation,
$P_{o} + \frac{1}{2} ρ V_{o}^{2} = P + \frac{1}{2} ρ V^{2}$
$P_{o} + \frac{1}{2} ρ V_{o}^{2} = P + \frac{1}{2} 16 ρ V_{o}^{2};$
$P = P_{o} - \frac{15}{2} ρ V_{o}^{2}$

Suggest Corrections

Similar questions

Q. An incompressible non-viscous fluid (density

δ

) flows steadily through a cylindrical pipe which has radius

2

R at point A and radius R at point B(at the same height as A) further along the flow direction. If the velocity and pressure at point A are v and P, respectively, find the pressure at B.

Q. An incompressible fluid flows steadily through a cylindrical pipe which has radius

2 R

at point A and radius

R

at point B farther along the flow direction. If the velocity at point

A

v

, its velocity at point B is

Q. A water pipe 4 cm in diameter has a constriction if diameter 2 cm. Find the rate of discharge of water through the pipe of the velocity of flow of water in the main pipe is 6 cm/s. Find also the velocity of flow at the constriction.

(75.36 \times 10^{- 6} m^{3} / s; 24 c m / s)

Q. An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius

2 R

at point

A

and radius

R

at point

B

farther along the flow direction. If the velocity of the fluid at point

A

V

, its velocity at the point

B

will be :

Q. An incompressible fluid is flowing steadily through a horizontal pipe of non-uniform cross section. If pressure of water is

4 \times 10^{4} N . m^{- 2}

at a point where cross section is

0.02 m^{2}

and velocity of flow is

2 m s^{- 1}

, the pressure at a point of cross sectional area

0.01 m^{2}

N . m^{- 2}

is :

Join BYJU'S Learning Program

An incompressible fluid of density ρ flows through a horizontal pipe of radius r and then passes through a constriction of radius r2 . If the fluid has pressure Po and velocity Vo before the constriction, pressure in the constriction is Po−3α2ρV2o. Here α is an integer. Find α .

By equation of continuity, πr2Vo=πr24V V=4Vo By Bernoulli's equation, Po+12ρV2o=P+12ρV2 Po+12ρV2o=P+1216ρV2o; P=Po−152ρV2o

By equation of continuity,
$π r^{2} V_{o} = π \frac{r^{2}}{4} V$
$V = 4 V_{o}$
By Bernoulli's equation,
$P_{o} + \frac{1}{2} ρ V_{o}^{2} = P + \frac{1}{2} ρ V^{2}$
$P_{o} + \frac{1}{2} ρ V_{o}^{2} = P + \frac{1}{2} 16 ρ V_{o}^{2};$
$P = P_{o} - \frac{15}{2} ρ V_{o}^{2}$