Question

A 60-cm-high, 40-cm-diameter cylindrical water tank is being transported on a level road. The highest acceleration anticipated is 4 m/s^2. Determine the allowable initial water height in the tank if no water is to spill out during acceleration.

Answer 1

`h_(max) = 51.8 cm`

Step-by-step explanation:

given data:

height of tank = 60cm

diameter of tank =40cm

accelration = 4 m/s2

suppose x- axis - direction of motion

z -axis - vertical direction

`\theta` = water surface angle with horizontal surface

`a_x =`accelration in x direction

`a_z =`accelration in z direction

slope in xz plane is

`tan\theta = (a_x)/(g +a_z)`

`tan\theta = (4)/(9.81+0)`

`tan\theta =0.4077`

the maximum height of water surface at mid of inclination is

`\Delta h = (d)/(2) tan\theta`

`=(0.4)/(2)0.4077`

`\Delta h  0.082 cm`

the maximu height of wwater to avoid spilling is

`h_(max) = h_(tank) -\Delta h`

= 60 - 8.2

`h_(max) = 51.8 cm`

the height requird if no spill water is
`h_(max) = 51.8 cm`