An open tank holds water 1.25 m deep. If a small hole of cross section area 3cm^2 is made at the bottom of the tank, calculate the mass of water per second initially flowing out of the hole. (g=10m/s^2, density of water= 1000 kgm^-3)
Sice you are still showing no work, my advice will be brief.
Use the Bernoulli equation (with altitude change)to get the velocity and the continuity equation to get the mass flow rate.
Don't know how to solve it!pleas help me out
Mass of water flowing out per second = mv
v is the velocity of the water coming out of the hole.
Since 'm' = V¶
Where 'V' is the volume of hole
'¶' is the density of water flowing out.
Therefore,mass of water flowing out per second= 0.03*1000*√2*10*1.25
=150kg/sec
To calculate the mass of water per second initially flowing out of the hole, we need to determine the volume of water flowing out per second and then multiply it by the density of water. Here's how you can calculate it step by step:
1. Start by calculating the volume of water flowing out per second. We can use Torricelli's law, which states that the velocity of the liquid flowing out of an orifice equals the velocity of a free-falling body from the same height. The formula is:
v = sqrt(2gh)
where:
v is the velocity of water flowing out,
g is the acceleration due to gravity (10 m/s^2),
and h is the height of the water above the hole.
In this case, h = 1.25 m. Substitute these values into the formula:
v = sqrt(2 * 10 * 1.25)
v = sqrt(25)
v = 5 m/s
So, the velocity of water flowing out of the hole is 5 m/s.
2. Next, calculate the volume of water flowing out per second using the formula:
Volume = Area * Velocity
The area of the hole is given as 3 cm^2, but we need to convert it to square meters. Since 1 cm = 0.01 m, the area is:
Area = 3 cm^2 * (0.01 m/cm)^2
Area = 0.03 m^2
Now, multiply the area by the velocity:
Volume = 0.03 m^2 * 5 m/s
Volume = 0.15 m^3/s
Therefore, the volume of water flowing out per second is 0.15 m^3/s.
3. Lastly, calculate the mass of water per second by multiplying the volume by the density of water:
Mass per second = Volume * Density
The density of water is given as 1000 kg/m^3, so:
Mass per second = 0.15 m^3/s * 1000 kg/m^3
Mass per second = 150 kg/s
Hence, the mass of water per second initially flowing out of the hole is 150 kg/s.