Question

one end of a two dimenssional water tank has the shape of a quadrant of a circle of radius 2m. when the tank is full, the vertical component of the force per unit length on the curved surface will be​

Answer 1

Step-by-step explanation:

Let the length is L

so the total volume of the liquid contained in it is given as

V = \frac{\pi r^2}{4} LV=

4

πr

2

L

V = \frac{\pi (2^2)}{4} LV=

4

π(2

2

)

L

V = \pi LV=πL

now the weight of the liquid contained in it

W = \rho VW=ρV

W = (1000)(\pi L) kgfW=(1000)(πL)kgf

so vertical force by the curved surface will balance the weight of the liquid

so we have

F = 1000\pi LF=1000πL

now force per unit length is given as

\frac{F]{L} = 1000\pi kg f