An ideal fluid of density 800 ; kg cdot m^{-3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) From the equation of continuity,$A_1 v_1 = A_2 v_2$. Given $A_1 = a$ and $A_2 = \frac{a}{2}$,we have $a v_1 = \frac{a}{2} v_2$,which implies $v_2

Vedclass · Accepted Answer

$363$

Vedclass · Answer

(A) From the equation of continuity,$A_1 v_1 = A_2 v_2$. Given $A_1 = a$ and $A_2 = \frac{a}{2}$,we have $a v_1 = \frac{a}{2} v_2$,which implies $v_2 = 2 v_1$. Applying Bernoulli's theorem between the two sections: $P_1 + ho g h_1 + \frac{1}{2} ho v_1^2 = P_2 + ho g h_2 + \frac{1}{2} ho v_2^2$. Taking the lower section as reference level $(h_2 = 0)$,then $h_1 = 1 \; m$. $P_1 - P_2 = ho g (h_2 - h_1) + \frac{1}{2} ho (v_2^2 - v_1^2)$. Substituting the given values: $4100 = 800 	imes [10 	imes (0 - 1) + \frac{1}{2} ( (2v_1)^2 - v_1^2 )]$. $4100 = 800 	imes [-10 + \frac{3 v_1^2}{2}]$. $\frac{4100}{800} = -10 + \frac{3 v_1^2}{2}$. $5.125 = -10 + 1.5 v_1^2$. $15.125 = 1.5 v_1^2$. $v_1^2 = \frac{15.125}{1.5} = \frac{121}{12}$. $v_1 = \sqrt{\frac{121}{12}} = \frac{11}{\sqrt{12}} = \frac{11 \sqrt{3}}{6} = \frac{\sqrt{121 	imes 3}}{6} = \frac{\sqrt{363}}{6}$. Comparing this with $\frac{\sqrt{x}}{6}$,we get $x = 363$.

Similar Questions

Water is filled in a cylindrical container to a height of $3 \ m$. The ratio of the cross-sectional area of the orifice and the beaker is $0.1$. The square of the speed of the liquid coming out from the orifice is ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.

Why does an airplane run a certain length on the runway first before taking off?

An aeroplane of mass $4.5 \times 10^4 \,kg$ and total wing area of $600 \,m^2$ is travelling at a constant height. The pressure difference between the upper and lower surfaces of its wings is (Acceleration due to gravity $= 10 \,m \,s^{-2}$)

Bernoulli's principle is based on the law of conservation of

Why do two rowing boats moving parallel to each other come closer (attract) to each other?

Vedclass Test Series

Exam Paper Generator

Online Exam Module