The fluid flows horizontally in ##+\hat i## upto bend so force on it must be in direction of its velocity to make it flow and its reaction force on pipe must be in ##-\hat i##
After the bend the fluid flows in ##-cos37\hat i+sin37\hat j## and reaction force will be in opposite direction
Reaction forces due to oil pressure:
$$\vec F_1=P_1A_1 \hat i=-56\times 10^3\hat i$$
$$\vec F_2=P_2A_2=(8.6\times 10^3) \cos37\hat i-(8.6\times 10^3)\sin 37\hat j$$
Net force on pipe =Sum of Reaction force due to oil pressure= $$|\vec F_1+\vec F_2|=\sqrt{(56000-860\times 8)^2+(860\times...
The pressure is easily calculated from equation of continuity and Bernoullis theorem:
$$A_1v_1=A_2v_2\implies v_2=16ms^{-1}$$
SInce pipe is in horizontal plane, no difference in pressure because of height
$$P_1+\frac{\rho v_1^2}{2}=P_2+\frac{\rho v_2^2}{2}$$
$$P_2=172\times 10^3$$
What I...
The equation of ellipse reduces to :
$$(2x+3)^2+(3y+2)^2=8$$
$$\frac{(x+3/2)^2}{8/4}+\frac{(y+2/3)^2}{8/9}=1$$
Center of ellipse =##\left(\frac{-3}{2},\frac{-2}{3}\right)##
##b^2=a^2(1-e^2)=8/9## and ##a^2=8/4##
Therefore ##e=\frac{\sqrt{5}}{3}##
Distance between foci=##\frac{2\sqrt{10}}{3}##...
So I know I have to equate force on a hemispherical shell with spring force to get value of compression but I can't find the force on the hemispheres
Some places that do have the solution use the formula :
$$\text{Field of non-conducting hemispherical shell= } \frac{\sigma}{2\epsilon_○} $$
This...
But isn't it equating the force required for rotation to force exerted? I don't know if there is something like Centripetal pressure that is necessary for rotation
I am not sure I understand. The water can't be treated as rectangular/cylindrical blocks with forces ##V\rho g## on either side and arbitrary force due pressure in-between❓️
I think I got it
$$\int^b_0{\omega^2 A\rho rdr}-PA=A(b)\rho g$$
$$\int^{2b}_0{\omega^2A\rho rdr}-PA=A(3b)\rho g$$
Therefore
Subtracting equation 1 from 2
$$\frac{3A\rho\omega^2b^2}{2}=2Ab\rho g$$
So it will be
$$\int{\omega^2r dm}= V\rho g$$
On either side with limits ##0\text{ to }b## and ##0\text{ to }2b## and ##V## changed according to height of liquid column