Calculate the speed with which water flows from a hole in the dam of a large irrigation canal. The hole is 0.80 m below the surface of the water. If the hole has a radius of 2.0 cm, what is the flow rate of the water from the hole?
2 A circular dam has a radius of 10 m and a height of 3 m. Of the dam will be filled
with water from a pipe with an inside diameter of 10 cm and a water flow of 10
litres per second, calculate the time taken to fill the dam to a point 10 cm from the
top of the dam.
To calculate the speed at which water flows from a hole in the dam, we can use Torricelli's Law, which states that the speed of efflux (velocity) of a fluid through an orifice is given by the equation:
V = √(2gh)
Where:
V is the velocity of the efflux (flow rate) in m/s
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the vertical distance from the surface of the water to the hole in meters
In this case, the vertical distance h is given as 0.80 m.
Now, to determine the flow rate of the water from the hole, we can use the equation for the flow rate (Q), which is the volume of fluid passing through per unit time:
Q = Av
Where:
Q is the flow rate in m^3/s
A is the cross-sectional area of the hole in m^2
v is the velocity of the efflux in m/s
First, we need to convert the radius of the hole from centimeters to meters. Since the radius is given as 2.0 cm (later square it to get the area), we divide this value by 100 to convert it to meters. Thus, the radius (r) becomes:
r = 2.0 cm / 100 = 0.02 m
Now, we can calculate the cross-sectional area of the hole:
A = πr^2
Substituting the value of the radius, we get:
A = π(0.02 m)^2
Next, we can substitute the values of A and V into the flow rate equation to find Q:
Q = Av = (π(0.02 m)^2)(√(2gh))
Finally, plug in the values for g and h, and calculate Q.
Bernoulli's equation:
mgh=1/2 m v^2
v=1.6g
flow rate: I assume you mean mass flow rate, not volume rate.
flow rate=density*velocity*areahole