At two points 1 and 2 in a pipeline the velocities are V and 2V- respectively- Both the points are at the same elevation- The fluid density is - The flow can be assumed to be incompressible- inviscid- steady and irrotational- The difference in pressures P1 and P2 at points 1 and 2 is

Applying Bernoulli's equation, we get P_1ρ g+(V)^22g+Z=P_2ρ g+(2V)^22g+Z ⇒ P_1 P_2ρ g=4V^2 V^22g ⇒ P_1 P_2=32ρ V^2 ⇒ P_1 P_2=1.5ρ V^2 ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Fluid Mechanics

Bernoulli Equation-II

At two points...

Question

At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is $ρ$ . The flow can be assumed to be incompressible, inviscid, steady and irrotational. The difference in pressures P $_{1}$ and P $_{2}$ at points 1 and 2 is

0.5 ρ V^{2}

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

1.5 ρ V^{2}

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

2 ρ V^{2}

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

3 ρ V^{2}

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

Open in App

Solution

The correct option is B $1.5 ρ V^{2}$
Applying Bernoulli's equation, we get
$\frac{P_{1}}{ρ g} + \frac{(V)^{2}}{2 g} + Z = \frac{P_{2}}{ρ g} + \frac{(2 V)^{2}}{2 g} + Z$
$\Rightarrow \frac{P_{1} - P_{2}}{ρ g} = \frac{4 V^{2} - V^{2}}{2 g}$
$\Rightarrow P_{1} - P_{2} = \frac{3}{2} ρ V^{2}$
$\Rightarrow P_{1} - P_{2} = 1.5 ρ V^{2}$

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. Three points

A, B

and

C

on a steady flow of a non viscous and incompressible fluid are observed. The pressure, velocity and height of the points

A, B

and

C

are

(2, 3, 1) . (1, 2, 2)

and

(4, 1, 2)

respectively. Density of the fluid is

1 k g m^{- 3}

and all otner parameters are given in SI units. Then which of the following is correct?

(g = 10 m s^{- 2})

Q. A horizontal tube has different cross sections at point

A

and

B

. The areas of cross section are

a_{1}

and

a_{2}

, respectively, and pressures at these points are

p_{1} = ρ g h_{1}

and

p_{2} = ρ g h_{2}

, where

ρ

is the density of liquid flowing in the tube and

h_{1}

and

h_{2}

are heights of liquid column in vertical tubes connected at

A

and

B

. If

h_{1} - h_{2} = h

, then the flow rate of the liquid in the horizontal tube is :

Q. In the given figure,

P_{1}

and

P_{2}

are the pressure experienced at the points

1

and

2

on a charged conductor respectively. Then:

Q. Consider a flow through a nozzle, as shown in the figure below

The air flow is steady, incompressible and inviscid. The density of air is 1.23

k g / m^{3}

. The pressure difference

(p_{1} - p_{a t m}

) is ______kPa (round off to the nearest integer).

Join BYJU'S Learning Program

At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is ρ. The flow can be assumed to be incompressible, inviscid, steady and irrotational. The difference in pressures P1 and P2 at points 1 and 2 is

The correct option is B 1.5ρV2Applying Bernoulli's equation, we get P1ρg+(V)22g+Z=P2ρg+(2V)22g+Z ⇒ P1−P2ρg=4V2−V22g ⇒ P1−P2=32ρV2 ⇒ P1−P2=1.5ρV2