Fluids and Conservation Laws (Continuity, Bernoulli) Practice

Sample questions

5 of 12 — sign in to practice the rest with adaptive difficulty and mastery tracking.

1. Sample 1difficulty 1/5

   An iron block sinks in water because

   • A

     Iron is heavier than water

   • B

     Iron's density exceeds water's density

     check_circle
   • C

     Iron does not displace water

   • D

     Buoyancy is zero

   Why

   "Heavier" is ambiguous; what matters is <strong>density</strong>. Iron is denser than water, so its weight exceeds the maximum possible buoyant force (full submersion).

   View full solution & statsarrow_forward

2. Sample 2difficulty 2/5

   Water flows through a pipe whose radius drops from $r_1 = 4~\text{cm}$ to $r_2 = 2~\text{cm}$. If the speed in the wide section is $1.0~\text{m/s}$, the speed in the narrow section is

   • A

     $0.25~\text{m/s}$

   • B

     $4.0~\text{m/s}$

     check_circle
   • C

     $0.50~\text{m/s}$

   • D

     $2.0~\text{m/s}$

   Why

   Continuity: $A_1 v_1 = A_2 v_2$, with $A \propto r^2$: $v_2 = (r_1/r_2)^2 v_1 = 4 \cdot 1.0 = 4.0~\text{m/s}$.

   View full solution & statsarrow_forward

3. Sample 3difficulty 2/5

   Water flows from a pipe at $0.60~\text{m/s}$ through cross-section $0.020~\text{m}^2$. How long to fill a $300~\text{L}$ tank?

   • A

     $25~\text{s}$

     check_circle
   • B

     $15~\text{s}$

   • C

     $50~\text{s}$

   • D

     $100~\text{s}$

   Why

   Volume rate: $A v = 0.012~\text{m}^3/\text{s}$. $300~\text{L} = 0.30~\text{m}^3$. $t = 0.30/0.012 = 25~\text{s}$.

   View full solution & statsarrow_forward

4. Sample 4difficulty 2/5

   Water flows through a pipe that narrows from cross-sectional area $A_1 = 0.040~\text{m}^2$ (speed $2.0~\text{m/s}$) to $A_2 = 0.010~\text{m}^2$. What is the speed in the narrow section?

   • A

     $2.0~\text{m/s}$

   • B

     $8.0~\text{m/s}$

     check_circle
   • C

     $0.5~\text{m/s}$

   • D

     $4.0~\text{m/s}$

   Why

   Continuity (incompressible): $A_1 v_1 = A_2 v_2 \Rightarrow v_2 = (0.040/0.010)(2.0) = 8.0~\text{m/s}$.

   View full solution & statsarrow_forward

5. Sample 5difficulty 2/5

   A hydraulic lift uses pistons of areas $0.005~\text{m}^2$ (input) and $0.10~\text{m}^2$ (output). To support a $2000~\text{N}$ car on the output, the input force is

   • A

     $50~\text{N}$

   • B

     $2000~\text{N}$

   • C

     $100~\text{N}$

     check_circle
   • D

     $40{,}000~\text{N}$

   Why

   Same pressure: $F_1/A_1 = F_2/A_2 \Rightarrow F_1 = (0.005/0.10) \cdot 2000 = 100~\text{N}$.

   View full solution & statsarrow_forward