A bus has windows that have become partly filled with rain water (p,\" 1000kg /

Question

A bus has windows that have become partly filled with rain water (p," 1000kg / m3). one window is 2m long, lm high and with a gap between the two glass panes of 5mm. If the window is on the side of the bus (parallell to the direction of trave) and filled to half-height (0.5m) with water, calculate the following: Hint: + at: u a,-at 1. Evaluate the maximum pressure due to liquid pressure acting on the inside of the glass when the bus is initially stopped. Where is this location on the window? (10 points) The bus accelerates horizontally (instantly) from zero velocity such that the slope of water between the window panes is 0.1:1 (vertical:horizonta. Evaluate the acceleration of the bus. (10 points) 2.

Explanation / Answer

given bus windows

rhow = 1000 kg/m^3

l = 2m

h = 1m

d = 5 mm

y = 0.5 m

1. maximum pressure due to liquid pressure acting on the4 inside of the wall when the bus is initially stopped = Pmax

Pmax = Po + rho*g*y = 1.01*10^5 + 1000*9.81*0.5 = 105905 Pa

this location is the bottom most point of the window

2. slope , tan(theta) = 0.1/1

theta = 5.710593137 deg

acceelration of bus = a

tan(theta) = a/g

a = g*tan(tjheta) = 0.981 m/s/s

3. in this configuration

maximum height of the fluid = H

minimum height = h

then

H = 0.5 + 1*sin(theta) = 0.5995037 m

Pmax = Po + rho*g*H = 106881.1314835 Pa

4. a1 = 0.1g

a2 = 0.05g

a3 = 0.025g

v1 = a1*5 = 0.5g

v2 = 0.5g + 0.05g*5 = 0.75g

v3 = 0.75g + 0.025*5 = 0.875g

hence maximum velocity = 8.58375m/s

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