A horizontal oriented tube AB of length 5m rotates with a constant angular velocity 0.5 rad/s about a stationary vertical axis OO' passing through the end A. the tube is filled with ideal fluid. The end of the tube is open, the closed end B has a very small orifice. The velocity with which the liquid comes out from the hole (in m/s) is
A horizontal oriented tube AB of length 5m rotates with a constant angular velocity 0.5 rad/s about a stationary vertical axis OO' passing through the end A. the tube is filled with ideal fluid. The end of the tube is open, the closed end B has a very small orifice. The velocity with which the liquid comes out from the hole (in m/s) is
Text Solution
Verified by Experts
Apply bernoullie theorem between two ends
`P_(0)+rhounderset(3)overset(5)intxomega^(2)dx=P_(0)+(1)/(2)rhov^(2)implies(rho omega^(2))/(2)[5^(2)-3^(2)]=(1)/(2)rhov^(2)implies(0.5)2xx16=v2impliesv-2m//s`
`P_(0)+rhounderset(3)overset(5)intxomega^(2)dx=P_(0)+(1)/(2)rhov^(2)implies(rho omega^(2))/(2)[5^(2)-3^(2)]=(1)/(2)rhov^(2)implies(0.5)2xx16=v2impliesv-2m//s`
Topper's Solved these Questions
ELASTICITY, SURFACE TENSION AND FLUID MECHANICS
ALLEN |Exercise Exercise 1 (Elasticity)|16 VideosELASTICITY, SURFACE TENSION AND FLUID MECHANICS
ALLEN |Exercise Exercise 1 (Surface Tension)|21 VideosCENTRE OF MASS
ALLEN |Exercise EXERCISE-V B|19 VideosERROR AND MEASUREMENT
ALLEN |Exercise Part-2(Exercise-2)(B)|22 Videos
Similar Questions
Explore conceptually related problems
A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity omega about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is
A thin uniform rod of mass .M. and length .L. rotates with constant angular velocity .omega. about perpendicular axis passing through its centre. Two bodies each of mass (M)/(3) are attached to its two ends. What is its angular velocity?
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass m is dropped a the centre and is allowed to spread out and finally fall. The angular velocity during this period ...........
A metallic rod of length I rotates at angular velocity omega about an axis passing through one end and perpendicular to the rod. If mass of electron is m and its charge is -e then the magnitude of potential difference between its two ends is
Two blocks of mass m_(1)=10kg and m_(2)=5kg connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of the turntable. The coefficient of friction between the table and m_(1) is 0.5 while there is no friction between m_(2) and the table. the table is rotating with an angular velocity of 10rad//s . about a vertical axis passing through its center O . the masses are placed along the diameter of the table on either side of the center O such that the mass m_(1) is at a distance of 0.124m from O . the masses are observed to be at a rest with respect to an observed on the tuntable (g=9.8m//s^(2)) . (a) Calculate the friction on m_(1) (b) What should be the minimum angular speed of the turntable so that the masses will slip from this position? (c ) How should the masses be placed with the string remaining taut so that there is no friction on m_(1) .
A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with an angular velocity 400rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) tenstion in the rod and (b) the elogation of te rod. The density of material of the rod is 10^(4)kg//m^(3) and the young's modulus is 2xx10^(11)N//m^(2)
A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity omega is an example of non=inertial frame of reference. The relationship between the force vecF_(rot) experienced by a particle of mass m moving on the rotating disc and the force vecF_(in) experienced by the particle in an inertial frame of reference is vecF_(rot)=vecF_(i n)+2m(vecv_(rot)xxvec omega)+m(vec omegaxx vec r)xxvec omega . where vecv_(rot) is the velocity of the particle in the rotating frame of reference and vecr is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter fo a disc of radius R rotating counter-clockwise with a constant angular speed omega about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis (vecomega=omegahatk) . A small block of mass m is gently placed in the slot at vecr(R//2)hati at t=0 and is constrained to move only along the slot. The distance r of the block at time is
A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity omega is an example of non=inertial frame of reference. The relationship between the force vecF_(rot) experienced by a particle of mass m moving on the rotating disc and the force vecF_(in) experienced by the particle in an inertial frame of reference is vecF_(rot)=vecF_(i n)+2m(vecv_(rot)xxvec omega)+m(vec omegaxx vec r)xxvec omega . where vecv_(rot) is the velocity of the particle in the rotating frame of reference and vecr is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter fo a disc of radius R rotating counter-clockwise with a constant angular speed omega about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the x-axis along the slot, the y-axis perpendicular to the slot and the z-axis along the rotation axis (vecomega=omegahatk) . A small block of mass m is gently placed in the slot at vecr(R//2)hati at t=0 and is constrained to move only along the slot. The distance r of the block at time is
The cylindrical tube of a spray pump has a cross-section of 8 cm^2 , one end of which has 40 fine holes each of area 10^-8 m^2 . If the liquid flows inside the tube with a speed of 0.15 m min^-1 , the speed with which the liquid is ejected through the holes is.
A 1.0 m long metallic rod is rotated with an angular frequency of "400 rad s"^(-1) about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
ALLEN -ELASTICITY, SURFACE TENSION AND FLUID MECHANICS-Exercise 5 B (Integer Type Questions)
- A horizontal oriented tube AB of length 5m rotates with a constant ang...
Text Solution
|
- Two soap bubbles A and B are kept in a closed chamber where the air is...
Text Solution
|
- A cylindrical vessel of height 500mm has an orifice (small hole) at it...
Text Solution
|
- Consider two solid spheres P and Q each of density 8gm cm^-3 and diame...
Text Solution
|