A rectangular prismatic tank has the following dimensions :length is 3 m, width is 2m . And depth is 3m .it is being filled with water and the surface level is rising at 20cm/min.what is the inflow rate of water at the tank ?
To find the inflow rate of water into the tank, we need to calculate the volume of water being added per unit time.
First, let's calculate the volume of the tank. Since it is a rectangular prismatic tank, we can use the formula:
Volume = length x width x depth
Given:
length = 3 m
width = 2 m
depth = 3 m
Plugging in the values:
Volume = 3 m x 2 m x 3 m
Volume = 18 m^3
Now, let's convert the rising surface level into meters. Since the surface level is rising at 20 cm/min, we need to convert cm to meters:
20 cm = 0.2 m (since 1 m = 100 cm)
The rising surface level of 0.2 m/min represents the increase in volume of water per minute.
To find the inflow rate of water, we divide the increase in volume (0.2 m^3/min) by the cross-sectional area of the tank, which is the product of length and width:
Inflow rate = Increase in volume / (length x width)
Inflow rate = 0.2 m^3/min / (3 m x 2 m)
Inflow rate = 0.2 m^3/min / 6 m^2
Inflow rate = 0.0333 m/min
Therefore, the inflow rate of water into the tank is approximately 0.0333 m/min.
Ok, volume= 1/2*width*height*length
but the width of the top is 2/3 * height
volume= 1/2 *2/3 h^2*length
dv/dt=2/3 h*length dh/dt
You are given dh/dt, compute dv/dt. Now note that you cant answer this unless you know the depth at that time.