Question

Bernoulli's equation is given by $P+\frac{1}{2}\rho v^2+h\rho g=k,$ where $P=$ pressure, $\rho$ = density, $v=$ speed, $h=$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant.
The dimensional formula for $k$ is same as that of

• A. velocity gradient
• B. pressure gradient
• C. modulus of elasticity
• D. thrust

Answer 1

The correct option is C modulus of elasticity

Step 1,

$k$ is dimension ally equivalent to $P.$

Now we can write

Dimension formula for $k$ is

$k=\left[M^1{L}^{-1}{T}^{-2}\right]$

Step 2,

We know,

Modulus of elasticity is $=\frac{\text{Stress}}{\text{Strain}}=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}=\frac{Fl}{A\Delta l}$

Dimension formula for Modulus of elasticity is $=\frac{\left[M{L}^1{T}^{-2}\right]\left[L^1\right]}{\left[L^2\right]\left[L^1\right]}=\left[M{L}^{-1}{T}^{-2}\right]$