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Chapter 9: Problem 39

A 5 -m-diameter parachute of a new design is to be used to transport a load from flight altitude to the ground with an average vertical speed of $3 \mathrm{m} / \mathrm{s}$. The total weight of the load and parachute is 200 N. Determine the approximate drag coefficient for the parachute.

Short Answer

Expert verified
The approximate drag coefficient for the parachute is 0.56.

Step by step solution

01

Determine the Surface Area of the Parachute

The surface area \( A \) of the parachute can be calculated using the formula for the area of a circle which is \( A = \pi \times (d/2)^2 \), where \( d \) is the diameter of the parachute. The diameter of the parachute is given as 5 m, so the surface area will be \( A = \pi \times (5/2)^2 =19.63 \, m^2 \).
02

Apply the Drag Force Equation

The parachute descends at a constant speed, meaning that the drag force is equal to the weight of the parachute. Hence, we can write the drag equation as such: \( 200 = 0.5 \times \rho \times 19.63 \times C_D \times (3)^2 \). Here, \( \rho \) is assumed to be the standard air density at sea level, \(1.225 m^{-3}\). Therefore, the equation becomes: \( 200 = 0.5 \times 1.225 \times 19.63 \times C_D \times 9 \).
03

Solve for the Drag Coefficient

Re-arranging the equation to find \( C_D \), we find that \( C_D = \frac{200}{0.5 \times 1.225 \times 19.63 \times 9} = 0.56 \).

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Most popular questions from this chapter

A model is placed in an airflow at standard conditions with a given velocity and then placed in water flow at standard conditions with the same velocity. If the drag coefficients are the same between these two cases, how do the drag forces compare between the two fluids?

Compare the rise velocity of an \(\frac{1}{8}\) -in.-diameter air bubble in water to the fall velocity of an \(\frac{1}{8}\) -in.- -diameter water drop in air. Assume each to behave as a solid sphere.

A design group has two possible wing designs \((A \text { and } B\) ) for an airplane wing. The planform area of either wing is \(130 \mathrm{m}^{2}\) and each must provide a lift of \(1,550,000 \mathrm{N}\)

A sail plane with a lift-to-drag ratio of 25 flies with a speed of 50 mph. It maintains or increases its altitude by flying in thermals, columns of vertically rising air produced by buoyancy effects of nonuniformly heated air. What vertical airspeed is needed if the sail plane is to maintain a constant altitude?

As is discussed in Section \(9.3,\) the drag on a rough golf ball may be less than that on an equal-sized smooth ball. Does it follow that a 10 -m-diameter spherical water tank resting on a \(20-\mathrm{m}\) -tall support should have a rough surface so as to reduce the moment needed at the base of the support when a wind blows? Explain.
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