Again consider the model propeller of the previous problem. If we assume the jet velocity to be equal to the velocity of the air through the propeller, then we can say that m=roh A Vj , where roh is the air density, A is the propeller area and Vj is the speed of the flow through the propeller.
Given that the test was performed with an air density of 1.225 kilograms per cubic metre, determine the propeller diameter (in metres).
Would it change is the calculated mass was 0.720kg/s
Yes, in that case, the propeller diameter would be different. Let's redo the calculation using the new mass flow rate:
m = 0.720 kg/s
A = m/(rohVj)
We still have roh = 1.225 kg/m^3 from the previous information. However, we need to determine Vj in order to solve for A.
From the previous problem, we know that the thrust force generated by the propeller is 7.84 N. We can use this information to solve for the speed of the flow through the propeller using the equation for thrust:
T = mVj + (Vj - Vp)A(rohVj)
where Vp is the speed of the propeller and all other variables are as defined previously.
Since the propeller is stationary in our case, Vp = 0. Therefore, the equation simplifies to:
T = mVj
Solving for Vj, we get:
Vj = T/m
Substituting the given values, we have:
Vj = 7.84 N/0.720 kg/s
Vj ≈ 10.89 m/s
Now we can solve for A:
A = m/(rohVj)
A = 0.720/(1.225 x 10.89)
A ≈ 0.055 m^2
Finally, we can calculate the propeller diameter:
d = √(4A/π)
d = √(4 x 0.055/π)
d ≈ 0.334 m or 33.4 cm
Therefore, the propeller diameter is approximately 33.4 cm if the mass flow rate is 0.720 kg/s instead of 0.8 kg/s.
To find the propeller diameter, we need to know the values of m (mass flow rate) and Vj (speed of the flow through the propeller).
However, the problem does not provide any information about the mass flow rate or the speed of the flow through the propeller. So, it is not possible to calculate the propeller diameter with the given information.
To solve this problem, we would need additional data such as the mass flow rate or the speed of the flow through the propeller.
We are not given enough information to directly solve for the propeller diameter. However, we can use the given information to set up an equation using the area of a circle:
A = π (d/2)^2
where A is the propeller area and d is the diameter of the propeller. We can rearrange this equation to solve for d:
d = √(4A/π)
Substituting the given values, we have:
m = rohAVj
A = m/(rohVj)
A = 0.8/(1.225 x 60) [from previous problem]
A = 0.01057 m^2
d = √(4 x 0.01057/π)
d ≈ 0.115 m or 11.5 cm
Therefore, the propeller diameter is approximately 11.5 cm.