GATE 2011 AEROSPACE ENGINEERING (Q 31-40)

  1. A rocket engine is tested on a test bed under the ideal condition of fully expanded jet. The exhaust velocity is 2 km/s through a nozzle of area 2.5 m2. The mass flow rate is 200 kg/s. The specific impulse of the propellant and the thrust developed respectively are (assume g = 9.81 m/s2)
    1. 175.87 s and 200 kN
    2. 203.87 s and 400 kN
    3. 231.87 s and 200 kN
    4. 280.87 s and 400 kN

    Answer:- 280.87 s and 400 kN

  2. A body undergoes deformation under plane strain conditions when subjected to the following stresses (in MPa): σxx=450, σyy=450, τxy=75, τxz=0, τyz=0. What are the remaining components of stresses (in MPa) and strains? Assume the material to be isotropic and linear-elastic with Young’s modulus E=200 GPa and Poisson’s ratio ν=1/3.
    1. σzz=0, εxx=0.00225, εyy=0.00225, γxy=0.002, γxz=0, γyz=0
    2. σzz=300, εxx=0.001, εyy=0.001, γxy=0.001, γxz=0, γyz=0
    3. σzz=300, εxx=0.00225, εyy=0.00225, γxy=0.001, γxz=0, γyz=0
    4. σzz=0, εxx=0.001, εyy=0.001, γxy=0.002, γxz=0, γyz=0

    Answer:- σzz=300, εxx=0.001, εyy=0.001, γxy=0.001, γxz=0, γyz=0
    For plain strain condition, εzz=0
    ⇒ (1/E)[σzz-ν(σxxyy)]=0
    ⇒ σzz=ν(σxxyy)
    ⇒ σzz=(1/3)(450+450)=300 MPa
    εxx=(1/E)[σxx-ν(σyyzz)]
    ⇒ εxx=(1/200000)[450-(1/3)(450+300)]
    ⇒ εxx=0.001
    εyy=(1/E)[σyy-ν(σzzxx)]
    ⇒ εyy=(1/200000)[450-(1/3)(300+450)]
    ⇒ εyy=0.001
    Shear Modulus G=E/[2(1+ν)]
    γxyxy/G
    ⇒ γxy=2τxy(1+ν)/E
    ⇒ γxy=(2)(75)[1+(1/3)]/200000=0.001
    For plain strain condition, γxz=0, γyz=0

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s