HARD
JEE Main/Advance
IMPORTANT
Earn 100

Two U-tube manometers are connected to the same tube as shown in the figure. Determine difference of pressure between X and Y. Take specific gravity of mercury as 13.6. (g=10 m s-2, ρHg=13600 kg m-3 )

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Important Questions on Fluid Mechanics

HARD
JEE Main/Advance
IMPORTANT
A rectangular vessel is filled with water and oil in equal proportion (by volume), the oil being twice lighter than water. Show that the force on each sidewall of the vessel will be reduced by one fifth if the vessel is filled only with oil. (Assume atmospheric pressure is negligible)
MEDIUM
JEE Main/Advance
IMPORTANT
A cube of wood supporting a 200 gm mass just floats in water. When the mass is removed the cube rises by 2 cm at equilibrium. Find side of the cube.
MEDIUM
JEE Main/Advance
IMPORTANT

A metallic square plate is suspended from a point x as shown in the figure. The plate is made to dip in water such that the level of water is well above that of the plate. The point x is then slowly raised at constant velocity. Sketch the variation of tension T in string with the displacement s of point x

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MEDIUM
JEE Main/Advance
IMPORTANT
Calculate the rate of flow of glycerin of density 1.25 x103 kg m-3 through the conical section of a pipe placed horizontally, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N m-2.
HARD
JEE Main/Advance
IMPORTANT

Consider the Venturi tube of figure. Let area A equal 5a. Suppose the pressure at A is 2.0 atm. Compute the values of velocity v at A and velocity v' at a that would make the pressure p at 'a' equal to zero. Compute the corresponding volume flow rate if the diameter at A is 5.0 cm. (The phenomenon at a when p falls to nearly zero is known as cavitation. The water vaporizes into small bubbles.) (Patm = 105 N m-2, ρ= 1000 kg m-3).

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MEDIUM
JEE Main/Advance
IMPORTANT

Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at x and y are 40 mm2 and 20 mm2 respectively. If 10 cc of water enters per second through x, find

(i) the speed of the water at x,

(ii) the speed of the water at y and

(iii) the pressure difference Px  Py

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MEDIUM
JEE Main/Advance
IMPORTANT

Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at x and y are 40 mm2 and 20 mm2 respectively. If 10 cc of water enters per second through x, find

(i) the speed of the water at x,

(ii) the speed of the water at y and

(iii) the pressure difference Px  Py

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Suppose the tube in the previous problem is kept vertical with x upward but the other conditions remain the same. The separation between the cross-section at x and y is 1516 cm. Repeat parts (i), (ii) and (iii) of the previous problem. Take g=10 m s-2.

MEDIUM
JEE Main/Advance
IMPORTANT

Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at x and y are 40 mm2 and 20 mm2 respectively. If 10 cc of water enters per second through x, find

(i) the speed of the water at x,

(ii) the speed of the water at y and

(iii) the pressure difference Px  Py

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Suppose the tube in the previous problem is kept vertical with y upward. Water enters through y at the rate of 10 cm3 s-1. Repeat part (iii). Note that the speed decreases as the water falls down.