Solved GATE Questions on Fluid Statics
Question 1. The horizontal and vertical hydrostatic forces on the semi-circular gate, having a width w into the plane of figure, are
(A)
(B)
(C)
(D)
GATE-ME-2001
Hint 1. (Ans D)
Question 2. A water container is kept on a weighing balance. Water from tap is falling vertically into the container with a volume flow rate of Q; the velocity of water when it hits the water surface is U. At a particular instant of time the total mass of the container and water is m. The force registered by the weighing balance at this instant of time is
(A)
(B)
(C)
(D)
GATE-ME-2003
Hint 2. (Ans A)
Volume of flow rate =Q
Mass of water strike=
Velocity of water when it hit the water surface =U
Force on weighing balance due to water strike
=Initial momentum-Final momentum
=
=
(Since final velocity is perpendicular to initial velocity)
Now total force on weighing balance=mg+
Question 3. A cylindrical body of cross-sectional area A, height H and density , is immersed to depth h in a liquid of density , and tied to the bottom with a string. The tension in the string is
(A)
(B)
(C)
(D)
GATE-ME-2003
Hint 3. (Ans D)
Let T= Tension in string
Question 4. The pressure gauge installed on the system show pressures of . The value of unknown pressure P is
(A) 1.01 bar
(B) 2.01 bar
(C) 5.00 bar
(D) 7.01 bar
GATE-ME-2004
Hint 4. (Ans B)
Question 5. A closed cylinder having a radius R and height H is filled with oil of density . If the cylinder is rotated about its axis at an angular velocity of , then thrust at the bottom of the cylinder is
(A)
(B)
(C)
(D)
GATE-ME-2004
Hint 5. (Ans D)
We know that
Area of circular ring=2
Force on elementary ring=intensity of pressureArea of ring
Thrust at the bottom of the cylinder =weight of water in the cylinder + total force on the top of the cylinder
Question 6. A U-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations A and B in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of the mercury is 13600 and g=9.81 . Which of the following is correct?
(A) Flow direction A to B and
(B) Flow direction is B to A and
(C) Flow direction is A to B and
(D) Flow direction is B to A and
GATE-ME-2005
Hint 6. (Ans A)
As pressure is decreasing from A to B,
So flow direction is A to B.
Question 7. For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?
(A) Metacentre should be below centre of gravity.
(B) Metacentre should be above centre of gravity.
(C) Metacentre and the centre of gravity must lie on the same horizontal line.
(D) Metacentre and centre of gravity must lie on the same vertical line.
GATE-ME-2010
Hint 7. (Ans B)
For stable equilibrium meta centre should be above the centre of gravity
Question 8. A hinged gate of length 5m, inclined at 30° with the horizontal and with water mass on its left, is shown in the figure below. Density of water is 1000 . The minimum mass of the unit width (perpendicular to the plane of paper), required to keep it closed is
(A) 5000
(B) 6000
(D) 7546
(D) 9623
GATE-ME-2013
Hint 8. (Ans D)
Let us solve it by
Pressure diagram (here it is triangular prism)
F= Volume of diagram
Taking moments about hinge
1. (D) 2. (A) 3. (D) 4. (B) 5. (D) 6. (A) 7. (B) 8. (D)