In case of streamline flow of a fluid (which is incompressible), consider these streamlines A, B and C (as shown in the figure) Let, P, Q and R are 3 planes perpendicular to the direction of flow of streamlines, then which of the following is correct?

Question

In case of streamline flow of a fluid (which is incompressible), consider these streamlines A, B and C (as shown in the figure)

Let, P, Q and R are 3 planes perpendicular to the direction of flow of streamlines, then which of the following is correct? (A) mP>mQ>mR, where m= mass flow per second. (B) vP>vQ>vR (C) nP>nQ>nR, where n= number of fluid particles crossing area per unit time. (D) mP < mQ < mR

Tardigrade Admin · Accepted Answer

Mass of fluid flowing out is equals the mass flowing in, therefore

Δ m_{P} = Δ m_{Q} = Δ m_{R}

, we have

A_{P} v_{P} ρ_{P} Δ t = A_{Q} v_{Q} ρ_{Q} Δ t = A_{R} v_{R} ρ_{R} Δ t

...(i)
For flow of incompressible fluids, we have,

ρ_{P} = ρ_{R} = ρ_{Q}

Thus, Eq. (i) reduces to,

\Rightarrow A_{P} v_{P} = A_{R} v_{R} = A_{Q} v_{Q}

Also, from the given figure we can also say that,

A_{R} > A_{Q} > A_{P}

So, at narrower portions, where the streamlines are closely spaced, velocity increases.
i.e.

v_{p} > v_{O} > v_{R}

Q. In case of streamline flow of a fluid (which is incompressible), consider these streamlines $A, B$ and $C$ (as shown in the figure)

Let, $P, Q$ and $R$ are 3 planes perpendicular to the direction of flow of streamlines, then which of the following is correct?

$m_{P} > m_{Q} > m_{R}$ , where $m =$ mass flow per second.

$v_{P} > v_{Q} > v_{R}$

$n_{P} > n_{Q} > n_{R}$ , where $n =$ number of fluid particles crossing area per unit time.

$m_{P} < m_{Q} < m_{R}$

Q. In case of streamline flow of a fluid (which is incompressible), consider these streamlines A,B and C (as shown in the figure) Let, P,Q and R are 3 planes perpendicular to the direction of flow of streamlines, then which of the following is correct?

mP​>mQ​>mR​, where m= mass flow per second.

vP​>vQ​>vR​

nP​>nQ​>nR​, where n= number of fluid particles crossing area per unit time.

mP​<mQ​<mR​

Q. In case of streamline flow of a fluid (which is incompressible), consider these streamlines $A, B$ and $C$ (as shown in the figure)

Let, $P, Q$ and $R$ are 3 planes perpendicular to the direction of flow of streamlines, then which of the following is correct?

$m_{P} > m_{Q} > m_{R}$ , where $m =$ mass flow per second.

$v_{P} > v_{Q} > v_{R}$

$n_{P} > n_{Q} > n_{R}$ , where $n =$ number of fluid particles crossing area per unit time.

$m_{P} < m_{Q} < m_{R}$