Ethyl alcohol flows through a horizontal tube of diameter 2.96
cm that is joined to a second horizontal tube of diameter 1.50
cm. The pressure difference between the tubes is 7.41 kPa.
What is the speed of flow in the first tube?
what grade r u in~~~~.....
And did your teacher explain thhis to u because u should know it!!!
To find the speed of flow in the first tube, we can use the principle of continuity equation, which states that the flow rate of an incompressible fluid is constant along a horizontal pipe if the pipe has a constant diameter. The equation can be written as:
A1V1 = A2V2
Where:
A1 is the cross-sectional area of the first tube
V1 is the speed of flow in the first tube
A2 is the cross-sectional area of the second tube
V2 is the speed of flow in the second tube
The cross-sectional area of a tube can be calculated using the formula:
A = πr²
Where:
A is the cross-sectional area
r is the radius of the tube
In this case, we are given the diameter of both tubes. We can find the radius by dividing the diameter by 2.
Given:
Diameter of the first tube (D1) = 2.96 cm
Radius of the first tube (r1) = D1 / 2
Diameter of the second tube (D2) = 1.50 cm
Radius of the second tube (r2) = D2 / 2
Now, let's calculate the cross-sectional areas of both tubes:
A1 = πr1²
A2 = πr2²
Next, we need to calculate the speed of flow in the second tube. We are given the pressure difference between the two tubes, which we can use to calculate the difference in height (h) using the formula:
h = (P2 - P1) / ρg
Where:
P2 - P1 is the pressure difference between the tubes
ρ is the density of ethyl alcohol
g is the acceleration due to gravity
We can assume the density of ethyl alcohol (ρ) is known.
Finally, with the height difference (h), we can use the Bernoulli's equation to find the speed of flow in the second tube:
V2 = √(2gh)
With all the information, we can substitute the values into the continuity equation (A1V1 = A2V2) to solve for V1, which is the speed of flow in the first tube.