Two different fluids (i.e., 1 and 2) flow over two identical flat plates with same free stream velocity. The ratio of viscosities of fluids is 1.5. The fluid 1 is twice as dense as second. Now, consider flow is laminar throughout the plate length. The ratio of drag force for plate (1) to plate (2) is _____.(Answer correct upto two decimal places.)
1.15

Open in App

Solution

The correct option is A 1.15
Drag force, $F_{D} = \frac{1}{2} C_{D} ρ A V^{2}$
$F_{D} \propto C_{D} ρ$ (A and V is constant)
$\frac{μ_{1}}{μ_{2}} = 1.5$ and $\frac{ρ_{1}}{ρ_{2}} = 2$ (Given)
$C_{D} = \frac{1.328}{\sqrt{R_{e_{1}}}} = \frac{1.328}{\sqrt{\frac{ρ V L}{μ}}}$ (For laminor flow)
$\Rightarrow C_{D} \propto \sqrt{\frac{μ}{ρ}}$
$\Rightarrow F_{D} \propto C_{D} \times ρ$
$\Rightarrow F_{D} \propto \sqrt{\frac{μ}{ρ}} \times ρ$
$\Rightarrow \begin{matrix} F_{D} \propto \sqrt{μ ρ} \end{matrix}$
$\frac{(F_{D})_{1}}{(F_{D})_{2}} = \sqrt{\frac{ρ_{1} μ_{1}}{ρ_{2} μ_{2}}}$
$= \sqrt{1.5 \times 2} = \sqrt{3} = 1.732$

Suggest Corrections

Similar questions

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity of 3 m/s. With the assumptions of Newtonian fluid, steady and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to

$\frac{d^{2} u}{d y^{2}} = 0$

If the dynamic viscosity of the lower fluid $μ_{2}$ , is twice that of the upper fluid $μ_{1},$ then the velocity at the interface (round off to two decimal places) is m/s.

Q. For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is

Q. For the fluid flowing over a flat plate with Prandtl number greater than unity, the thermal boundary layer for laminar forced convection.

Q. The velocity profile of a fluid over a flat plate is parabolic in nature. At a distance of

15 cm

from the plate, the velocity of fluid is maximum i.e

100 cm/s

. Calculate the shear stress at a distance of

10 cm

from the plate if the viscosity of the fluid is

10 poise

Q. A smooth flat plate is in a parallel flow stream. The ratio of the drag over the upstream half of the plate to that over the entire plate is ... Assume the average skin friction coefficient is proportional to

(R e_{x})^{- 1 / 2}

Join BYJU'S Learning Program

The correct option is A 1.15Drag force, FD=12CDρAV2 FD∝CDρ (A and V is constant) μ1μ2=1.5 and ρ1ρ2=2 (Given) CD=1.328√Re1=1.328√ρVLμ (For laminor flow) ⇒CD∝√μρ ⇒FD∝CD×ρ ⇒FD∝√μρ×ρ ⇒FD∝√μρ (FD)1(FD)2=√ρ1μ1ρ2μ2 =√1.5×2=√3=1.732