Question

A cylindrical bucket sitting on the edge of a table has a 2.95 mm diameter hole near the bottom. Water squirts out the hole as shown in the figure below. If the height of the table is H = 2.00 m, determine the height h of the water level in the bucket.

The answer is not 15.23 cm

Answer 1

Given

   cylindrical bucket diameter d = 2.95mm

   on a table , on the table is of height H = 2.00 m

now time taken by water to reach ground is S= vt+ 1/2 gt^2

   initial velocity is zero, then dy = 0.5gt^2

       t = sqrt(2*Delta y/g)

       t = Sqrt(2*2/9.8) s
       t = 0.36788   s

   v = Dx/Dt ====> v = 0.8/0.3677 m/s = 2.1757 m/s

by usign berbouli's equation

   P1+ 0.5 *v1^2 = P2+0.5rho*v^2 =
       here P1= P2=P
              
  
equating the light string is rho*g*y1 = 0.5rho*g*y1 +rv^2

here h = y2-y1

and simlofied Bernoulli's vquation

   y1-y2 = h = v2^2/2 g = 2.1757^2/(2*9.8) m

                H = 0.2415138005102 M