Question

A 10 meter tall tank open to the air is filled with a fluid with a density of 1200 kg/m3. It is located with its bottom 10 meters off the ground. When a hole is open at the bottom, fluid sprays out with an initial horizontal velocity. Determine how far (initially) the fluid sprays horizontally before it touches the ground

Answer 1

20 m

Step-by-step explanation:

First find the initial horizontal velocity. Use conservation of energy or Bernoulli equation.

PE at top of tank = KE at exit

mgh = ½ mv²

v = √(2gh)

v = √(2 × 9.8 m/s² × 10 m)

v = 14 m/s

Next, find how long it takes the stream to fall. Given in the y direction:

s = 10 m

u = 0 m/s

a = 9.8 m/s²

Find: t

s = ut + ½ at²

10 = (0) t + ½ (9.8) t²

t = 1.43 s

Finally, find the horizontal distance. Given in the x direction:

u = 14 m/s

a = 0 m/s²

t = 1.43 s

Find: s

s = ut + ½ at²

s = (14) (1.43) + ½ (0) (1.43)²

s = 20 m