Question

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 $1kg{m}^{-3}$ and all otner parameters are given in SI units. Then which of the following is correct? $(g=10m{s}^{-2})$

• A. points A and B lie on the same stream line
• B. point B and C lie on same stream line
• C. point C and A lie on same stream line
• D. None of the above

Answer 1

The correct option is D None of the above

Given : $\rho =1kg/m^3$

Using Bernoulli's theorem, $P+\rho gh+\frac{1}{2}\rho v^2=constant$

For point A : $2+1\left(10\right)\left(1\right)+\frac{1}{2}\times \left(1\right)\left(3^2\right)=16.5$

For point B : $1+1\left(10\right)\left(2\right)+\frac{1}{2}\times \left(1\right)\left(2^2\right)=23$

For point C : $4+1\left(10\right)\left(2\right)+\frac{1}{2}\times \left(1\right)\left(1^2\right)=24.5$

As the value of the constants are different in each case, thus all these points do not lie on same stream line.